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Now that U.S. forces have eliminated one of the most sought-after Al Qaeda chiefs, leaders in the United States, Iraq and across the world are trying to stay a step ahead of future terrorist actions with predictions and plans for a post-Abu Musab al-Zarqawi world.

Between calls for imminent troop reduction and speculation about who Zarqawi’s successor will be — with some in the military floating the name of Egyptian-born, Afghanistan-trained Abu al-Masri as his likely successor — two things are certain: The war in Iraq isn’t over yet and the insurgency hasn't ended.

Click here for complete coverage of Zarqawi's death.

"The foreign jihadists make up a very small percentage of the broader insurgency, and Al Qaeda is one group within that jihadist movement," Sen. Jay Rockefeller, D-W.Va., the ranking member on the Senate Intelligence Committee, explained in a statement released Thursday afternoon.

"The bulk of the insurgency is comprised of former regime elements and others who want to drive the United States out of Iraq," he said. "The next largest group contributing to the violence is the sectarian militias loyal to radical factions such as that of Muqtada al-Sadr. The jihadists are the smallest component with the least support among the Iraqi population."

In other words, the sectarian militias and Saddam loyalists will remain a threat going forward, and they are larger and have more sympathizers among Iraqis than Zarqawi's "Al Qaeda in Iraq" does.

At the White House, President Bush on Thursday said the death of Zarqawi was good news for ending the insurgency there, but he cautioned that difficult times still lie ahead — asking the American people to hang in there because of the likelihood of violent retaliation.

Though Zarqawi's killing "is a severe blow to Al Qaeda and it is a significant victory in the War on Terror ... we have tough days ahead of us in Iraq that will require the continuing patience of the American people," Bush said.

In London, British Prime Minister Tony Blair echoed Bush's sentiments, calling Zarqawi's removal "a strike against Al Qaeda in Iraq and therefore a strike against Al Qaeda everywhere," but warning that no one should be deluded into thinking the terrorism movement in Iraq will fall apart.

"We know that they will continue to kill, we know that there are many, many obstacles to overcome," he said at his monthly news conference Thursday.

United Nations Secretary General Kofi Annan called the death of Zarqawi a "relief."

“This is an individual who has been responsible for many heinous crimes, caused lots of problems in Iraq for the government and the people of Iraq — the people of Iraq who are afraid to step out, the people of Iraq who are only demanding peace, stability, and to have their streets back,” the U.N. Web site quoted Annan as saying in a press briefing Thursday.

Click Here to Read How the U.S. Got Abu Musab al-Zarqawi

“I think they will all be relieved that he is gone," Annan said. "And of course, we cannot pretend that that will mean the end of the violence. But it is a relief that such a heinous and dangerous man who has caused so much harm to the Iraqis is no longer around to continue his work.”

Last month, Annan welcomed the incoming Iraqi government led by Prime Minister Nouri al-Maliki and vowed that the U.N. would fully support it.

CIA Director Gen. Michael Hayden in April predicted that Zarqawi's death, when it happened, would split the already sprawling jihadist movement into even smaller pieces.

"The loss of key leaders like [Usama] bin Laden, [Ayman al-] Zawahiri and Zarqawi — especially if they were lost in rapid succession — could cause the jihadist movement to fracture even more into smaller groups, and would probably lead to strains and disagreements," Hayden, who was then No. 2 U.S. intelligence official, said during that speech.

Click here for the FBI's list of Most Wanted Terrorists

Violence in Iraq didn't dwindle Thursday following news of Zarqawi's demise; another car bomb in Iraq left at least 40 dead.

American, British, Iraqi and possibly Jordanian intelligence were all involved in tracking down the notorious terror mastermind Wednesday night at an isolated safehouse near the village of Baqouba, based on tips from senior leaders in Zarqawi’s own network. Nine others were also killed in the attack, according to U.S. Secretary of Defense Donald Rumsfeld.

Zarqawi — who has taken responsibility for scores of brutal bombings, beheadings and kidnappings in Iraq, Jordan and elsewhere — had the same $25 million price on his head as Usama bin Laden. No one is likely to be awarded the reward money since the United States is probably not going to give the cash to members of Zarqawi's own terror group.

Intelligence officials say they believe Zarqawi has cells or links to Muslim extremists worldwide, including Iraq, Afghanistan, Turkey, Spain, Saudi Arabia, Sudan, Syria, Pakistan and Kuwait.

Maj. Gen. William Caldwell, the chief U.S. military spokesman in Iraq, said he believes that al-Masri — whose name is an alias and means "father of the Egyptian" — is a likely Zarqawi successor.

"He's the most logical one out there, as you look at that structure and how they operate," Caldwell told reporters Thursday. "[He] probably came around 2002 to Iraq. Probably actually helped to establish maybe the first Al Qaeda cell that existed in the Baghdad area. And there's obviously a lot more, because we've been looking at him fairly closely for a while."

Al-Masri is believed to have been trained in Afghanistan before traveling to Iraq. He is thought to be an expert at building roadside bombs, which have been used extensively since the Iraq war began in March 2003 and are now the No. 1 cause of American military casualties there.

Still, al-Masri isn't a shoo-in, causing many to wonder if he really is the next terror leader in Iraq or not.

Al Qaeda in Iraq is decentralized, and most of those who would have been in line for the job of running it after he was ousted have either been killed or detained. White House press secretary Tony Snow said Thursday that the life expectancy of 'Al Qaeda in Iraq' leaders is not very long.

"What is happening — and we've seen this and we've heard reports of it, but I think this dramatizes it — [is] the Iraqi people are saying, 'We've had it with these guys. We've had it. We're not going take it anymore,'" Snow said. "That is an important step, and this is the kind of thing that can reinforce those who want to go ahead and stand up against terror in their midst."

Then there's the issue of whether or not Zarqawi spiritual leader Abu Abdul-Rahman al-Iraqi actually died along with him in the airstrike. The U.S. military and the Bush administration said he did.

View How Zarqawi's Death May Impact Al Qaeda

But an Al Qaeda Internet statement Thursday confirming Zarqawi's death was signed by a man with the same name, casting some doubt on al-Iraqi's death. One terrorism expert wondered if it was a case of mistaken identity.

"My perception is that if they released a statement in the name of Abu Abdul-Rahman al-Iraqi, then he is still around and, as the deputy head of Al Qaeda in Iraq, he presumably is the new leader," Evan Kohlmann, a New York-based terror consultant and founder of globalterroralert.com, told The Associated Press.

"It is possible that two guys have the same name ... Abu Abdul-Rahman al-Iraqi has never been identified as a spiritual leader, always as a military leader."

Caldwell said the U.S. military had discussed the succession question with the Iraqi government even before Zarqawi was killed in the air strike, during which two 500-pound bombs were dropped on his hideout.

Iraqi Prime Minister al-Maliki said Thursday it made no real difference.

"Whenever there is a new Zarqawi, we will kill him," al-Maliki told reporters.

But if the next Al Qaeda in Iraq leader is anything like the last, it won't be a simple task. It took the United States military and an emerging Iraqi security force three years to nab Zarqawi, and some outside observers say the Iraqi police force is still a hornet's nest of corruption that needs its stingers rooted out.

"We have a lot of work to do. We are making very, very good progress with the Iraqi army. We are not so good with the Iraqi police. They are about a year behind," said Rep. John Kline, R-Minn., who returned from Iraq on Monday. "We are working hard to have them catch up."

Thursday brought another positive development in the war in Iraq: the official installment of the new government there after months of disagreements and unrest about who should lead the Iraqi people.

Within minutes of the announcement of Abu Musab al-Zarqawi's death, Prime Minister al-Maliki named three key security ministers.

American lawmakers agree they have their work cut out for them in the months ahead. House Minority Whip Roy Blunt, R-Mo., said eliminating the terror leader "helps us a lot in the short run ... [but] we shouldn’t overestimate what this one incident means.”

Blunt said a top priority is removing the bands of outlaw militias roaming the country that are behind many of the bombings that have killed thousands of Iraqis, Americans and others working in Iraq.

Since the Iraqi government is so new, it will take time before they will be ready to rule without outside support, according to Kline.

"The government is coming on strong now, but we need to let this thing develop," he said. "When we pull our troops back, when we pull our troops out, this will be a free Iraq that can stand on its own feet.

“Al Qaeda itself as an organization is not eliminated," the former Marine added. "This is a war that we’re going to be in for some time.”

Sen. Joe Biden, D-Del., agreed, saying special attention needs to be paid to removing the insurgents within the Iraqi police and military forces.

"I urge the president to use Zarqawi's demise to push for three things to end the growing sectarian violence, which threatens to blow up into civil war," Biden said in a statement. "First, we must push the new ministers of Interior and Defense to purge the sectarian militias from the army and police."

Biden also said the White House should encourage the Iraqi government to amend the constitution by the deadline four months from now and ensure that the Sunni minority faction in the country is involved.

He said he also believes the United Nations and the United States should work together on a conference in the region to create and enforce an agreement that Iraq's neighbors will adhere to a hands-off policy.

Al Qaeda in Iraq tried to give the impression that it was energized, not deflated, by the news of Zarqawi's demise.

"The death of our leaders is life for us," said the Al Qaeda in Iraq statement. "It will only increase our persistence in continuing the holy war so that the word of God will be supreme."

Caldwell said he wouldn't be surprised if the group responds to Zarqawi's death by unleashing a barrage of attacks to assert its "viability" as a lasting network.

The Islamic militancy has been brought to new heights in recent years with the advent of the modern terror network. The terrorists have made clear their goal from the start: to drive out the "infidels," or "heathens" — in other words, non-Muslims — and to form a new Islamic regime throughout the Muslim world.

But some experts on Islamic extremism say they suspect a ready successor for Zarqawi, whose operation was seeing a steady decline recently because many top and middle managers had been captured or killed, may not be on deck.

Rime Allaf of London's Chatham House, an international affairs think tank, said a new leader was anyone's guess at this point.

"Recent statements had suggested some Al Qaeda figures were unhappy with the brutality of Zarqawi's attacks and his targeting of civilians," she told the AP. "It could be that his replacement, or replacements, will adopt a very different style."

In addition to continuing their fight against the militant resistance in Iraq, U.S. forces and contractors, Iraqis and others around the world who are helping in the reconstruction still have much to do in the way of rebuilding the country.

Water, electricity, schools, airports and roads all need to be in regular working order before Iraq will be viable on its own again. If the terror network is slowed, that effort can move up in priority.