left at least 14 people dead in the Abu Ghraib district in Baghdad Province, according to security officials. The New York times said in news briefed by “Shafaq News”.

Separately, in Ramadi, another battleground in the western Anbar Province, militants captured and executed four members of an elite military unit, an official said. And in Baghdad, two car bombs exploded near bus stations, killing at least 14 civilians.

The violence posed a further challenge to Iraq’s prime minister, Nuri Kamal al-Maliki, whose government has struggled for a response after Sunni insurgents, including fighters linked to Al Qaeda, captured Fallujah and parts of Ramadi almost two weeks ago. On Sunday, Mr. Maliki seemed to back away from earlier promises to mount an all-out military assault on Falluja, saying in an interview with the Reuters news agency that he wanted to “end the presence of those militants without any bloodshed.”

Instead of using the military, Mr. Maliki appeared to be leaning on Sunni tribal leaders to expel the militants themselves, and has been providing them with weapons and money for that purpose. The strategy appeared to reflect the pressure on Mr. Maliki from Iraqi political figures as well as American officials to avoid further inflaming sectarian tensions in Anbar, a region that has long complained of authoritarianism and unfair treatment by the Shiite-led government, the New York Times added.

At the same time, he suggested that the conflict might not end anytime soon. “We do not care how long this takes,” he said.

Iraq’s foreign minister, Hoshyar Zebari, said in an interview that the standoff could last months, given that Sunni militants who had been fighting in the Syrian civil war had joined the battle in western Iraq. “We will be in this for the long haul,” Mr. Zebari said. “Probably as long as Syria is going on.”

American military, intelligence and embassy officials had been unusually engaged in trying to defuse the crisis, including by mediating with Sunni leaders in Anbar Province, Mr. Zebari said. The Obama administration “feels that if this is not contained, it’s moving toward an all-out sectarian confrontation,” he said.

The fighting has left more than a hundred people dead and forced thousands of Falluja’s residents to flee the city, to Baghdad, northern Iraq and the southern city of Karbala, where Shiite leaders are hosting the displaced families in housing built for religious pilgrims.

Several of the refugees in Karbala said Sunday that they had little hope of returning home soon, and no clear notion of the identities of the gunmen fighting in their city — said to be a mix of tribesmen, Qaeda militants and others.

“We are caught in the middle,” said a resident who asked to be called Umm Abdullah, one of several who said they feared that Sunni militants would retaliate against them because they had fled to Karbala, a Shiite holy city.

Another refugee said militants burned down his house two days ago, after he was interviewed on television from Karbala.

Later on Sunday, gunmen attacked an army patrol in the Abu Ghraib district, as the fighting spilled beyond the borders of Anbar Province toward Baghdad. In heavy clashes that included military airstrikes, at least four soldiers and 10 civilians were killed, according to security and hospital officials.

The executions in Ramadi of the officers of the elite unit, the Special Operations Forces, apparently in retaliation to the government’s arrest of a Sunni lawmaker last month, threatened to touch off a new round of violence.

In a statement, Fadhel al-Barwari, a commander in the Special Operations Forces, pledged to “kill a thousand Al Qaeda members” for each of the soldiers, the newspaper concluded.