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The assassination of former Pakistani Prime Minister Benazir Bhutto on Thursday has led to dueling concerns in Washington of whether Pakistan's steps toward greater democracy will halt in their tracks and whether the country's military is strong enough to safeguard its nuclear arsenal and stanch further terror attacks.

The Bush administration is adhering to its position of calling for Pakistan to move forward with planned legislative elections on Jan. 8, and top congressional leaders did the same.

Administration officials also gave no indication that there would be any shifts in stance toward Pakistan's military, which has been a major ally in the War on Terror, largely due to its shared border with Afghanistan.

• FOX Facts: Benazir Bhutto

• Click here to view photos of Bhutto.

• Click here to view photos of the blast (WARNING: GRAPHIC CONTENT).

Yet some analysts expressed concern over the country's ability to maintain peace within its borders or prevent violence from spreading beyond.

President Bush on Thursday denounced Bhutto's assassination, which took place just as a political rally in Rawalpindi, Pakistan, was coming to a close. At least 20 others were killed as a result of a bomb blast, but Bhutto died after being shot in the neck and chest.

"The United States strongly condemns this cowardly act by murderous extremists who are trying to undermine Pakistan's democracy," Bush said, speaking from his ranch in Crawford, Texas. "Those who committed this crime must be brought to justice."

Bush: Assassins 'Must Be Brought to Justice'

• 2 U.S. Lawmakers Advised by State Department to Leave Pakistan, Were to Meet Bhutto

Bush also praised Bhutto's bravery and called on the country to continue its move toward broader democracy.

"Mrs. Bhutto served her nation twice as prime minister and she knew that her return to Pakistan earlier this year put her life at risk. Yet she refused to allow assassins to dictate the course of her country.

"We stand with the people of Pakistan and their struggle against the force of terror and extremism. We urge them to honor Benazir Bhutto's memory by continuing with the democratic process for which she so bravely gave her life."

TIMES OF LONDON: Who Killed Bhutto — The Main Suspects

Click to view international coverage of Bhutto's assassination

Click to watch live streaming video from DAWN TV

Bush also offered condolences to Bhutto's family and her supporters and family members of the others killed in the attacks, and "all the people of Pakistan on this tragic occasion."

At his appearance in Crawford, the president did not take any questions from reporters. He later spoke with Pakistani President Pervez Musharraf, according to White House spokesman Scott Stanzel.

Stanzel said the conversation was brief and the president offered his condolences to Musharraf. Secretary of State Condoleezza Rice also has spoken with Bhutto's husband and the new leader of Bhutto's political party.

Video: Click here to watch Greta Van Susteren's interview with Bhutto.

Video: Bhutto Killed in Attack

Top Democratic and Republican leaders called on Pakistan's leaders to move forward with its elections.

House Speaker Nancy Pelosi called Bhutto's death "a tragic setback for the restoration of democracy in Pakistan. ... Our nation must stand with the Pakistani people in their struggle for democracy and continue to press the Musharraf government to ensure that the coming election is free and fair."

And in the Senate, the top Republican agreed.

"Benazir Bhutto's bravery stands in stark contrast to the cowardice of those who remain committed only to chaos, murder and thwarting democracy in Pakistan," Senate Minority Leader Mitch McConnell said. "It is our expectation that President Musharraf and the Pakistani people will go forward with free and fair elections."

• FOX411: Bhutto's Last Words

Amy Kellogg: Remembering Benazir Bhutto

Bush administration officials and others around Washington began bracing themselves for the fallout from the death of a beloved — and controversial — leader in a country that is crucial to U.S. foreign policy and efforts to fight the War on Terror.

Bhutto had just returned to Pakistan in October following an eight-year exile. She was seeking to reclaim power in the country, and Thursday's assassination comes only two weeks before legislative elections are scheduled. Bhutto's party was expected to do well.

One of the top concerns to U.S. officials is the stability of the Pakistan military and its nuclear weapons stockpile. Musharraf is seen as politically weakened. He recently gave up his post as leader of the country's military in an attempt to appease opponents calling for greater steps toward democracy.

"Of all the countries in the world we've been most concerned about — Afghanistan, Iraq, Iran —clearly the most dangerous, unstable country has been Pakistan," FOX News contributor and former U.S. Ambassador to Morocco Marc Ginsberg said.

Former Secretary of State Madeleine Albright, speaking with MSNBC shortly after the attack, expressed sorrow over Bhutto's death and said the Pakistani people have suffered a loss.

"Pakistan is a place where all the problems come together in terms of having a nuclear weapon, terrorism, extremism, poverty. ... This has obviously made things even worse in the most tragic way because what Benazir Bhutto has been trying to do is to really give the Pakistani people a chance to express their views," said Albright, who served under President Clinton.

And questions undoubtedly will focus on Musharraf.

"If he didn't have a hand in it, how could he have let it happen?" one senior State Department official told FOX News, raising the question of whether Musharraf had enough power to prevent the attack.

Another area of focus is going to be the new leader of the Pakistani military, Gen. Ashfaq Kiyani, who received control of the army from Musharraf.

Kiyani recently stepped down as head of Pakistan's Inter Services Intelligence agency, and analysts in Pakistan say Musharraf chose his successor very carefully: Kiyani will continue Musharraf's policies and likely will be as pro-Western as Musharraf.

Musharraf had been reluctant to relinquish his army role because his power base resides in the military, not with the Pakistani people. In fact, public opinion polls in Pakistan show support for Musharraf has been in the single digits.

The Bush administration has been reaching out to Kiyani through back channels to ensure the protection of Pakistan's nuclear weapons and to have another leader "in the loop with Washington" if Musharraf were forced from power.

And top officials in the Pentagon and State Department have had an "open dialogue" with Kiyani in recent weeks.

State Department spokesman Tom Casey told reporters the administration believes the elections should go forward on time — calling them the "best antidote" to Thursday's violence. He said terrorists would win if the elections were postponed.

Casey would not address questions over whether U.S. officials had lost confidence in Pakistan's ability to fight terrorists — or whether the government had been infiltrated by radicals. But he said the assassination was "a blow to Pakistan's democratic development."

But observers had differing opinions over what should happen in Pakistan in the coming days.

Albright said she hoped Musharraf would hold elections as scheduled next month and would make a commitment to investigating Bhutto's death. But she said he should not declare emergency rule, which was only recently lifted following protests there.

"I think that the best-case scenario is if there is, in fact, calmness and President Musharraf orders an investigation and says that, you know, he will honor her legacy of wanting to have free and fair elections," Albright said.

"The worst case, I think, is if they now, in fact, institute martial law and a variety of aspects that go with that. ... The worst thing is for there to be a situation where there is more killing," Albright said.

Former CIA case officer Bob Baer, however, said he believes martial law would be best for Pakistan to tamp down on violence and prevent regional war from breaking out.

"Lock it down. It's in our interest," said Baer, who is the author of several books on the Middle East.

And former U.S. Ambassador to the United Nations John Bolton told FOX he believes moving toward elections in the aftermath of Bhutto's death is unsafe.

Noting the apparent attempted assassination Thursday on Nawaz Sharif, one of Bhutto's rivals and an opposition leader to Musharraf, Bolton said there's an apparent attempt to bring more instability to Pakistan.

"That is the circumstance under which you could have a radical Islamist regime come to power and get control of those nuclear weapons," Bolton said. "That's absolutely the worst-case scenario."

Given that there's the possibility that extremist elements of the military were involved in the assassination, Bolton said, "The last thing we need to do is have a further deterioration of the situation, which I think continued politicking would almost certainly bring about."

"The idea we should be pushing Pakistan into elections next month, I think, is fraught with peril for the United States," he added.

Joe Cirincione, a foreign policy analyst at the Center for American Progress, told FOX one of the primary concerns is if the military does splinter, noting that Usama bin Laden is believed to be hiding in Pakistan.

He said Musharraf should impose "a brief period of martial law, and that in doing so he (should)indicate that this is a transition back towards democratic elections."

Other lawmakers added their voices in support of Pakistan's democratic movement, although at least one Democrat called into question Bush administration policy over aid to Pakistan.

Calling the shooting a "senseless act," New Jersey Sen. Bob Menendez said: "I hoped that the Bush administration would have undertaken a better accounting of the billions of dollars sent to Pakistan in military and social aid.

"The administration has yet to adequately report if those funds have produced the desired results, or even if they have been kept out of enemy hands, but evidence on the ground suggests that Pakistan has become less stable since 9/11," Menendez continued.

"At this crucial time, the administration must undertake the kind of diplomatic surge necessary to ensure that democracy in Pakistan does not die, and it must insist on full accountability of military and development assistance to Pakistan, which up to this point has been absent."

Several other lawmakers weighed in, calling for peace and democracy.

"The assassination of Benazir Bhutto is terrible news for those who support a stabilized democracy in Pakistan, both in that country and around the world. Bhutto was a brave leader who was beloved by millions in Pakistan," said Sen. Russ Feingold, D-Wis., a member of the Senate Foreign Relations Committee.

"The questions surrounding her assassination should have direct bearing on both the future of democracy in Pakistan and the relationship we will have with a country that is so critical in the fight against global terrorism," Feingold said.

House Armed Services Committee Chairman Ike Skelton, D-Mo., said he's concerned about the country's stability.

"This is a tragic event. Her death will make Pakistan all the more unstable at a time when we need them to work closely with us to defeat Al Qaeda and Taliban insurgents," Skelton said.

Bhutto twice served as Pakistan's prime minister between 1988 and 1996. She had returned to Pakistan from an eight-year exile Oct. 18. Her homecoming parade in Karachi also was targeted by a homicide attacker, killing more than 140 people. On that occasion she narrowly escaped injury.

The United States had been at the forefront of foreign powers trying to arrange reconciliation between Bhutto and Musharraf, who resigned as army chief and lifted a state of emergency under heavy U.S. pressure in the hope it would put Pakistan back on the road to democracy.

Bhutto's return to the country after years in exile and the ability of her party to contest free and fair elections had been a cornerstone of Bush's policy in Pakistan, where U.S. officials had watched Musharraf's growing authoritarianism with increasing unease.

Those concerns were compounded by the rising threat from Al Qaeda and Taliban extremists, particularly in Pakistan's largely ungoverned tribal areas bordering Afghanistan. This is despite that Washington had pumped nearly $10 billion in aid into the country since Musharraf became an indispensable counter-terrorism ally after Sept. 11, 2001.

Irritated by the situation, Congress last week imposed new restrictions on U.S. assistance to Pakistan, including tying $50 million in military aid to State Department assurances that the country is making "concerted efforts" to prevent terrorists from operating inside its borders.

Under the law, which provides a total of $300 million in aid to Pakistan and was signed by President Bush on Wednesday, Secretary of State Rice also must guarantee Pakistan is implementing democratic reforms, including releasing political prisoners and restoring an independent judiciary.

The law also prevents any of the funds from being used for cash transfer assistance to Pakistan, but that stipulation already had been adopted by the administration.

Despite the congressional move, Richard Boucher, the assistant secretary of state for South and Central Asian affairs who had been instrumental in engineering the Bhutto-Musharraf reconciliation, said he had little doubt the administration would get the money.

FOX News' Mike Emanuel, Bret Baier, James Rosen and Chad Pergram and The Associated Press contributed to this report.