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Intelligence indicates as many as 2,500 al Qaeda fighters are now living in five training camps in the al-Jazeera area, according to two other senior Iraqi security officials. The officials, who spoke on condition of anonymity because they were not authorized to release the information, estimated that only 700 al Qaeda fighters were in Iraq when U.S. troops withdrew. Six months earlier, in June 2011, U.S. Defense Secretary Leon E. Panetta told the U.S. Senate that 1,000 al Qaeda remained in Iraq.

Earlier this summer, al Qaeda in Iraq launched a campaign dubbed “Breaking the Walls,” which aimed at retaking strongholds from which it was driven by the American military. Sabah al-Nuaman, spokesman for the government’s counterterror services, acknowledged that Iraqi forces have struggled to contain al Qaeda since the U.S. military’s departure.

Iraqi and U.S. officials agree that Iraqi forces have improved their ability to gain terrorism intelligence from informants and prisoners. But they still struggle to intercept technical communications such as al Qaeda’s cellphone calls, radio signals and Internet messages — one of the methods used by the U.S. military.

“The Iraqi efforts to combat terrorists groups have been negatively affected by the U.S. pullout, but we are trying our best to compensate and develop our own capabilities,” Mr. al-Nuaman said.

The U.S. withdrew its military as required under a 2008 security agreement negotiated during the White House administration of then-President George W. Bush.

President Obama considered leaving several thousand troops in Iraq past the 2011 withdrawal deadline, but negotiations disintegrated last fall when Baghdad refused to extend legal immunities to any U.S. combat troops remaining in Iraq, meaning they could have been prosecuted for defending themselves if under attack.

Republicans blame Mr. Obama, a Democrat, for failing to push Baghdad harder or to find a compromise that would have let U.S. troops remain in Iraq as a safeguard against al Qaeda and deteriorating Mideast stability. On Monday, GOP presidential candidate Mitt Romney accused the White House of wasting gains the U.S. made in Iraq.

There now are about 260 active-duty troops and civilian Defense Department employees who have diplomatic immunity to remain in Iraq to train security forces on military equipment that Baghdad bought from the United States. Among them are 28 U.S. special operations forces who have been training Iraqi counterterror soldiers in the capital. But the money for their posts runs out at the end of the year unless Congress agrees to restore their funding.

The two senior Iraqi security officials said al Qaeda fighters have been moving easily between Iraq and Syria in recent months to help Sunni rebels overthrow Syrian President Bashar Assad, whose Alawite religious sect is an offshoot of Shiite Islam. And in Anbar province, some fighters linked to al Qaeda have regrouped under the name of the Free Iraqi Army — an attempt to align themselves with the rebels’ Free Syrian Army.

Anbar tribal Sheikh Hamid al-Hayes, a retired security official who helped U.S. forces fight al Qaeda in Anbar at the height of the insurgency, said the Free Iraqi Army is recruiting fighters and planning to overthrow the Shiite-led government in Baghdad.

“They want to mimic the Syrian revolution,” he said.

Mr. al-Nauman, the counterterror spokesman, denied that and said the group is merely a subset of al Qaeda fighters who adopted the new name to “attract the support of the Iraqi Sunnis by making use of the strife going on in Syria.”

Al Qaeda in Iraq for years had a hot-and-cold relationship with the global terror network’s leadership. It was the Syrian civil war, now in its 19th month, that prompted global al Qaeda leader Ayman al-Zawahri in February to embrace the Iraqi insurgency in hopes of recruiting fighters and support against Mr. Assad.

Before that, in 2007, Mr. al-Zawahri and Osama bin Laden distanced themselves from the Iraqi militants for killing civilians instead of only targeting the U.S. military and other Western targets. Now, there’s little doubt that Mr. al-Zawahri’s appeal to al Qaeda in Iraq bolstered its legitimacy and injected confidence into the insurgency just as the U.S. troops left.

Associated Press writer Sameer N. Yacoub contributed to this report.