Hundreds of extremists were feared to be on the run in Iraq on Monday after al-Qaeda’s affiliate in the country launched a major assault on the infamous Abu Ghraib prison, offering a fresh boost to the group’s resurgent fortunes in Iraq and in Syria.

Iraq’s Interior Ministry said in a statement that an unspecified number of prisoners had escaped from Abu Ghraib but none from a second facility that also came under assault. In Washington, U.S. officials closely monitoring the jailbreak said the number of escapees was thought to be 500 to 600, including a significant number of al-Qaeda operatives.

Members of the Iraqi parliament who said they had been briefed by security officials asserted that the escapees included some top “emirs,” or leaders, of the al-Qaeda in Iraq franchise, many of whom had been captured by U.S. troops.

Iraq’s security forces set up checkpoints on highways leading west to Syria and Jordan and around Baghdad’s airport to snare fugitives. At least some prisoners were recaptured in the dragnet, according to Iraqi news media reports.

But even if the prisoners are recaptured, the scale of the attacks on the heavily guarded facilities reinforced an impression among many Iraqis that their security forces are struggling to cope with a resurgent al-Qaeda since U.S. forces withdrew in 2011, taking with them much of the expertise and technology that had been used to hold extremists at bay.

There was no formal assertion of responsibility for the Sunday night assaults on the prisons, but they bore the hallmarks of the Islamic State of Iraq and the Levant, and many extremist Web sites identified the attacks as the work of the al-Qaeda-affiliated group.

The jailbreak coincided with a relentless wave of bombings blamed on the extremist group that has killed hundreds of civilians in recent months, returning Iraq to levels of violence not seen since the 2007 surge of U.S. troops.

At least 46 Iraqis died over the weekend in bombings that targeted cafes and mosques, bringing to more than 450 the number killed this month. Twelve members of the security forces were killed in an ambush Monday in the northern province of Nineveh.

The gains of the surge are in jeopardy, said Aymenn al-Tamimi, a fellow with the Philadelphia-­based Middle East Forum who monitors extremist activity in Iraq and Syria.

“This is a significant milestone in the resurgence of al-Qaeda in Iraq,” he said. “A good deal of the progress achieved from 2006 onwards has essentially been undone now.”

The operation will also help accelerate the group’s ascendancy in Syria, where it has been rapidly expanding at the expense of more-moderate rebel groups, said Charles Lister of the London-based IHS Jane’s defense consultancy.

“There’s no underestimating the boost to morale,” he said. “The fact that the Islamic State has managed to secure territory of its own in northern Syria all adds to a gradual trend of increasing confidence and strength of al-Qaeda in Iraq and in Syria.”

Unless recaptured, he said, those who escaped in the jailbreak will add to the pool of experienced operatives sustaining al-Qaeda’s rising influence in both countries. Extremist Web sites said those who were freed include foreign fighters captured by the U.S. military in 2006 and 2007. It is likely that they would seek to join the war in Syria against President Bashar al-
Assad’s government at a time when foreign fighters are flocking there from across the region.

The prison attacks involved suicide bombers who were used to breach the walls, followed by sustained mortar fire, according to accounts from both sides.

The assault on Abu Ghraib — a facility west of Baghdad renowned as a detention center for dissidents during Saddam Hussein’s regime and as the site of abuses by American troops against suspected insurgents during the years that U.S. forces occupied Iraq — appears to have been the more successful of the two raids. There the assailants managed to briefly overrun the facility.

At the Taji prison north of the capital, the attackers were beaten back after a bloody battle in which the head of the facility died.

The government sent troops and helicopter reinforcements to the two sites. By daybreak Monday, it said, it had reestablished control over the prisons. At least 26 members of the security forces were killed, 38 others were wounded and dozens of prisoners were killed, the government said.

A State Department spokesman declined to comment Monday, other than to say that Iraqi officials are “in pursuit of the escaped prisoners to return them to captivity.”

Al-Qaeda’s Iraq affiliate has undergone a number of identity transformations since it announced its existence in 2004 to counter the U.S. occupation. In 2006, it rebranded itself as the Islamic State of Iraq. In April, it announced that it would henceforth use the name Islamic State of Iraq and the Levant, thereby extending the reach of its activities into Syria and absorbing another al-Qaeda affiliate, the Syrian group Jabhat al-Nusra.

After Jabhat al-Nusra rejected the name change and sought to assert itself as a separate, Syrian entity, the two groups have coexisted in an uneasy alliance in the northern provinces of Syria that are under the control of rebels.

The Islamic State has, however, rapidly encroached on Jabhat al-Nusra’s support base in many locations in northern Syria in recent weeks, analysts say. It has taken the lead in the most recent battles between Kurds and rebels in the two northeastern provinces of Raqqah and Hasakah, and it has gained ascendancy over many more-moderate rebel groups in Aleppo and Idlib provinces.

Sly reported from Beirut. Ahmed Ramadan in Beirut and Joby Warrick in Washington contributed to this report.