operating in neighboring Syria and, increasingly, in Iraq itself, The New York Times said in an article briefed by “Shafaq News”.

The role of the former inmates in fueling a new wave of Sunni jihad across the region is an unfortunate reminder of the breakdown of authority in Iraq since the United States departed in 2011, of the security vacuum that has spread around the region and of the continuing threat of Sunni-led terrorist groups that the United States said it was fighting during its occupation of Iraq.

The prison breaks also reflect the surging demand for experienced fighters, which led to a concerted effort by militant groups, particularly the Islamic State of Iraq and Syria, or ISIS, to seek them in the one place where they were held en masse — Iraq’s prison cells.

That group even had a name for its prison strategy, “Operation Breaking the Walls,” which unfolded during a 12-month campaign from July 2012 until a major break at Abu Ghraib, the main Iraqi prison, on the western outskirts of the capital, in July 2013. In all, American officials estimate, a few hundred of the escapees have joined the Islamic State of Iraq and Syria, several in senior leadership roles, the newspaper said.

While the group was already gaining strength in this period, an American counterterrorism official said, “The influx of these terrorists, who collectively have decades of battlefield experience, probably has strengthened the group and deepened its leadership bench.”

One such escapee was Abu Aisha, who declined to be identified by his full name and is now leading a group of Qaeda fighters on the western edge of Falluja, his hometown, which for nearly six weeks has been held by antigovernment Sunni fighters. With Falluja under siege, the American government has been rushing guns, ammunition and missiles to help the Shiite-dominated Iraqi security forces and allied tribal fighters retake the city, where so many American Marines once fought — and died — nearly 10 years ago.

Abu Aisha was a car mechanic before 2003 but found new purpose in fighting the Americans. Many detainees, himself included, he said, spent their time in prison learning the ways of militant Islam, studying the Quran and Shariah law and preparing to return to waging jihad once free, the newspaper added.

Abu Aisha was originally arrested by the Americans and then released from Camp Bucca, the infamous American prison in southern Iraq, in 2008. He was rearrested by the Iraqis in 2010.

“Finally, they put me in Abu Ghraib, and I again met some of the leaders and fighters I knew, including princes from Al Qaeda — Iraqis, Arabs and other nationalities,” he said. “Most of them had been at Bucca as well.”

One night last summer, as Abu Aisha sat in his cell waiting, as he did each day, for his date with the executioner, explosions and gunfire erupted and a familiar prison guard opened the doors to his cell and told him to leave immediately. With hundreds of others, Abu Aisha ran through the prison’s corridors until he escaped through a hole that had been blasted through a wall. He hopped into a waiting Kia truck that took him to freedom — and back to the battlefield.

Abu Aisha said leaders of the Islamic State of Iraq and Syria gave him a choice: leave and fight with them in Syria, or stay and fight in Iraq.

“Many of the leaders that I know went to Syria and the jihad there once they fled from Abu Ghraib,” he said in a recent interview. “Other fighters went there after a while because they felt they would be freer in Syria. I decided to stay with my group.”

The prison breaks, and the mayhem they helped fuel in Syria, also had the effect of altering the calculus of many Western officials toward the war there. In the beginning, they saw the conflict in the terms of a dictator — President Bashar al-Assad — brutally oppressing his largely peaceful opponents.

But after the Islamic State of Iraq and Syria took on an increasingly important role in the fighting there — often battling with more moderate insurgent groups, to the dismay of Al Qaeda, which broke ties with ISIS over the issue — Western powers were even more reluctant to intervene, the newspaper said.

Osama al-Nujaifi, the speaker of Iraq’s Parliament and the country’s most important Sunni politician, said that the escaped fighters “went to Syria to lead large fighting groups there.”

“So, people started thinking, Is Bashar better, or is Qaeda better?” he said.

Many Western experts have blamed Turkey’s open-door policy along its southern border with Syria for fostering the growth of the Islamic State of Iraq and Syria and other extremist groups. But Turkish officials have pushed back, citing intelligence reports that trace the growth of the group to the Iraqi prison breaks.

More than 600 prisoners are believed to have escaped in the largest of these sophisticated attacks, facilitated by corrupt prison guards who were easily bought, the officials said.

Two prison breaks in particular — the one at Abu Ghraib and the other, in September 2012, in the northern city of Tikrit — have had a significant impact on the group’s overall capacity to undermine Iraqi security and contributed to its expansion in Syria, the officials said.

In the Tikrit break, for instance, 47 death row detainees escaped, and they appear to have been instrumental in facilitating the group’s re-energizing and escalation of operations throughout 2013, according to Charles Lister, a visiting scholar at the Brookings Doha Center in Qatar, the newspaper added.

American officials said more than 500 prisoners escaped in the Abu Ghraib operation alone. They also say that “the majority” of the escapees had been originally detained by Iraqi forces, but acknowledged that large numbers — perhaps scores — had been captured during American operations in Iraq before the United States military left the country at the end of 2011.

Shaker Waheeb, perhaps the most dangerous Al Qaeda figure to emerge here recently, was one of those captured. Mr. Waheeb was studying computer science at a university in Anbar when the American invasion of Iraq led him to quickly change paths and fight the Americans. He was detained and held in Camp Bucca before being turned over to the Iraqis. He escaped from the prison in Tikrit in late 2012.

In Iraq, Mr. Waheeb has become something of a cult figure for up-and-coming jihadis — he has been referred to as the heir apparent to Abu Musab al-Zarqawi, the brutal Qaeda leader who was killed by American forces in 2006 — and public enemy No. 1 to the broader public. Iraqi officials have claimed more than once to have killed him, but today he is a key figure leading the fighting within Falluja. Last summer, he was seen on a grisly video executing three Shiite truck drivers on the side of a highway in the deserts of Anbar Province and was linked to an attack in which 14 Shiite truck drivers in Iraq were found beheaded.

Among the more moderate fighting groups within Syria, the prison breaks have helped stoke conspiracy theories that the Islamic State of Iraq and Syria, which has been fighting recently with the groups, is a pawn of the Assad government. While there is no evidence to back that up, some said they believed that the Syrian government — with assistance from the Iraqi government of Prime Minister Nuri Kamal al-Maliki, which has largely sided with Mr. Assad — helped orchestrate the escapes.

“By doing this, exporting more foreign fighters to Syrian territory, the Maliki government did Assad’s regime a favor by supporting his claim of fighting terrorism inside Syria,” said Abduljabbar Osso, a rebel leader in Aleppo who has been fighting with the Islamic State of Iraq and Syria.

Another rebel commander, Lt. Col. Ahmad al-Aboud, said that the moment his people heard about the prison escapes in Iraq, “We knew we would face more trouble after that.”

“We have always faced difficulties smuggling light weapons from Iraq to Syria through the Iraq border,” he said, “but it was very easy for ISIS to get full patrols of vehicles, weapons and fighters across to Syria.”

The Iraqi government has done little to explain how the prison breaks happened, although most agree that the inmates had help from the inside. Parliament members said that when they tried to investigate the Abu Ghraib break, they were stymied by security forces and top government officials.

“Unfortunately, the government did not allow us to even get close to the prison for a week,” said Shwan Muhammed, a Member of Parliament and one of the investigators.

Not all of the escaped prisoners returned to the fight, “ the newspaper concluded.