BAGHDAD — A confrontation between Iraqi insurgents and government forces in the western city of Falluja edged closer to the capital on Sunday, after clashes between militants and the army left at least 14 people dead in the Abu Ghraib district in Baghdad Province, according to security officials.

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 Falluja 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.