BAGHDAD - At least six Iraqis were killed during a joint Iraqi-American counterterrorism operation on the outskirts of Fallujah on Wednesday, in the deadliest incident involving U.S. troops since the United States declared an end to its combat operations in Iraq on Aug. 31.

Iraqi officials said eight civilians were killed, while the U.S. military said four suspected members of al-Qaeda in Iraq and two civilians died in a firefight that erupted as forces tried to capture a presumed member of the militant group who allegedly was responsible for attacks in the region.

The U.S. troops were sent as advisers to the Iraqi forces, American and Iraqi officials said. Despite the official end of the U.S. combat mission, about 4,500 U.S. Special Operations forces remain in Iraq.

Iraqi officials in Anbar province said U.S. and Iraqi troops began raiding houses at 3 a.m. in Jubil, about 30 miles west of Baghdad. Among the dead, they said, were a 70-year-old man and three of his sons, who were all asleep in their yard when they were killed by a grenade. A fourth son died at a hospital, the Iraqi officials said.

Troops also entered a second house in the area and killed Yaseen Kassar, a former Iraqi military commander, Iraqi officials said, as well as two people in a third house.

It was not immediately clear whether the troops had been looking for Kassar or any of the other people killed. Many Iraqi army commanders who were fired shortly after the 2003 U.S.-led invasion of Iraq later became insurgent leaders.

Late Wednesday, a U.S. military spokesman disputed the local Iraqi officials' account. Maj. Rob Phillips said that four suspected al-Qaeda militants were killed and three were wounded after security forces were fired upon as they approached the building they were targeting.

Iraqi forces fatally shot two residents as they emerged from their homes, reportedly armed, Phillips said, adding that four suspects were also arrested.

The incident could heighten tensions in Anbar province, which was among the strongholds of the Sunni insurgency between 2004 and 2007. As U.S. troops have thinned out in recent months, insurgent groups such as al-Qaeda in Iraq have sought to regain a foothold there.

"The security situation in Fallujah may deteriorate because of what happened today," said Abdulfattah Izghear, a local city council member. "We asked U.S. troops and the Iraqi government to explain this unjustified action and this naked aggression against civilians."

Iraqi Prime Minister Nouri al-Maliki, who is in charge of the Iraqi special forces, ordered an investigation of the incident, the state-run network al-Iraqiya reported.

zachariaj@washpost.com Special correspondents Othman al-Mukhtar in Fallujah and Aziz Alwan in Baghdad contributed to this report.