Updated

Terrorism is the biggest threat to Iraqis and coalition forces working to rebuild the country, particularly in regions where support for deposed leader Saddam Hussein was the strongest, U.S. military officials said Thursday.

"It's clearly a problem for us because of the sophistication of the attacks and because of their tactics to go after Iraqis," Gen. John Abizaid (search), who is in charge of U.S. Central Command (search), said during a Pentagon briefing.

The so-called "Sunni Triangle," (search) the Sunni Muslim area between the cities of Baghdad, Ramadi and Tikrit — Saddam's tribal home — has been the site of lethal violence against U.S. forces in Iraq and civilians aiding reconstruction efforts.

Abizaid said the terrorist threat is being fueled by extremists operating in that area.

"They are clearly a problem for us because of the sophistication of their attacks and because of what I would call their tactics to go after Iraqis," he said.

"Clearly, they're going after Iraqis that are cooperating with us. They're going after soft targets of the international community. They're still seeking to inflict casualties upon the United States."

The latest example of potential terrorists going after so-called "soft targets," or installations with little to no security, was Tuesday's truck bomb that destroyed the U.N. headquarters in Baghdad, killing 23 people and injuring at least 100 others. Earlier in the week, there were supposed sabotage attacks on Iraq's water and oil pipelines.

Defense Secretary Donald Rumsfeld (search), at the briefing with Abizaid, characterized that bombing as a terrorist act not unlike those that occur periodically worldwide.

"Terrorist activity has been going on in our world for a long time," he said. "It is going on today. There is hardly a month that goes by where there's not some relatively significant terrorist act that occurs somewhere."

Anti-American fighters pouring over the borders from countries such as Syria and Iran into Iraq aren't helping the problem, Abizaid said.

Rumsfeld said that while those fighters may not be sponsored by governments, some of Iraq's neighbors aren't stopping the terrorist migration.

"They clearly are not being stopped by the countries from which they're coming," Rumsfeld said.

The comments came after the military announced the capture of another one of Saddam's top henchmen, Ali Hassan al-Majid al-Tikriti, a general known as "Chemical Ali." (search)

"Chemical Ali" was Saddam's first cousin and a powerful Baath Party (search) official linked to some of the regime's most brutal acts. He was the King of Spades and No. 5 in the U.S. Army's deck of "55-Most Wanted" (search) playing cards.

Al-Majid, also known as "butcher of the Kurds," got his nickname by supervising chemical attacks upon Kurdish civilians the regime accused of aiding Iranian forces during the last years of the Iran-Iraq war. He has also been linked to crackdowns on Shiites (search) in southern Iraq, and was governor of Kuwait for part of Iraq's seven-month occupation of the country in 1990-1991.

There are indications al-Majid had been connected to anti-American activity in Iraq.

"Chemical Ali has been active in some ways in influencing people around him in a regional way," Abizaid said.

U.S. leaders had thought al-Majid was killed in an air strike in April on a house in southern Iraq.

Although Al-Majid's capture whittled down the list of Saddam supporters who posed the biggest threat to a new Iraq — 43 of the 55 most wanted have either been captured or killed — the remaining threat still consists of other remnants of Saddam's regime and their supporters.

Asked whether he saw links or signs of cooperation between remnants of Saddam's former Baath Party — believed to be behind much of the anti-American violence in Iraq — and terrorist groups entering Iraq, Abizaid said they are organized in similar ways but are not allies.

"I believe that there are some indications of cooperation in specific areas," he said. "Of course, ideologically they are not at all compatible. But on the other hand, you sometimes cooperate against what you consider a common enemy."

The foreign fighters issue is gaining prominence, particularly after Tuesday's U.N. bombing.

A previously unknown group, the Armed Vanguards of the Second Muhammad Army (search), claimed responsibility for that deadly bombing, Arab television station Al-Arabiya station reported Thursday.

"We say it proudly that we did not hesitate for one moment to kill Crusader blood," a faxed statement from the group said.

The statement pledged "to continue fighting every foreigner [in Iraq] and to carry out similar operations." It threatened U.S. forces and Arabs and Muslims who aid them and said Arab countries should not send troops to Iraq to serve in an international peacekeeping force.

Many experts said homicide bombings are not characteristic of Iraq and thought that perhaps foreign terrorists came in to plan the bombing but that Iraqis helped out.

"I think we probably are going to find a terrorist organization, possibly something out of Iran," Ret. Army Col. David Hunt, a Fox News military analyst, told The O'Reilly Factor. "This is not a Baathist type of thing where they've ever used this type of bomb attack … this looks like a terrorist attack."

Israel's ambassador to the United Nations said Thursday that the truck was from Syria. Neither Rumsfeld nor Abizaid would comment about that. FBI investigators on the scene have said the munitions used were Soviet-made, left over from the old regime.

But L. Paul Bremer (search), the U.S. civilian administrator in Iraq, said earlier this week that the possibility that militant Iraqis were responsible for the bombing should not be ruled out. He said more than 100 foreign terrorists were believed to be in Iraq.

Iraq's Governing Council (search) thinks Saddam loyalists are responsible, but more organized terror groups had a hand in the U.N. bombing.

Ahmad Chalabi (search), a prominent council member, warned that the lines between foreign militants and pro-Saddam guerrillas is already blurred, saying Iraqi intelligence reports showed that the Saddam's Fedayeen militia had allied itself with the Al Qaeda (search)-linked Ansar al-Islam (search).

"There is evidence of links between Fedayeen Saddam (search) and Ansar al-Islam," he told a news conference this week. "Ansar are now in Baghdad and they are comprised of Iraqis from all sects and non-Iraqis."

Abizaid backed up that theory Thursday, when he said the terrorist threat includes Ansar al-Islam, which has migrated south into the Baghdad area. U.S.-led forces destroyed an Ansar camp in northern Iraq during the early days of the war to oust Saddam.

Abizaid said terrorists are now firmly established in the Iraqi capital and pose a growing danger.

"Clearly, it is emerging as the number one security threat," he said. "And we are applying a lot of time, energy and resources to identify it, understand it and deal with it."

The Associated Press contributed to this report.