BAGHDAD — U.S. and Iraqi forces exchanged fire with suspected Sunni insurgents today, killing two and wounding four of them during a massive search for three missing American soldiers in a volatile area south of Baghdad, the Iraqi army said.

An al-Qaida front group, the Islamic State in Iraq, claimed Sunday that it had captured U.S soldiers in a deadly attack on a U.S. convoy the day before in Sunni area south of Baghdad that is known as the “triangle of death” — a longtime al-Qaida stronghold.

Meanwhile, 4,000 U.S. troops backed by aircraft, intelligence units and Iraqi forces were scouring the farming area around Mahmoudiya and the nearby town of Youssifiyah for the third day, as the military promised to make every effort available to find the missing soldiers.

Lt. Col. Christopher Garver, a U.S. military spokesman in Baghdad, said the military could not verify the claim by the Islamic State of Iraq.

The Islamic State in Iraq offered no proof for its claim on Internet that it was behind the attack Saturday in Mahmoudiya, about 20 miles south of Baghdad, that also killed four U.S. soldiers and an Iraqi translator.

On Sunday, U.S. troops surrounded Youssifiyah and told residents over loudspeakers to stay inside, residents said. They then methodically searched the houses, focusing on possible secret chambers under the floors where the soldiers might be hidden, residents said.

The soldiers marked each searched house with a white piece of cloth.

Soldiers also searched cars entering and leaving the town, writing “searched” on the side of each vehicle they had inspected. Several people were arrested, witnesses said.

Early this morning, U.S. and Iraqi forces exchanged fire with gunmen near Youssifiyah during the house-to-house search operation for the missing American soldiers, killing two suspected insurgents and injuring four others, a top Iraqi army officer in the area said.

He said the fighting began at about 3:30 a.m. and lasted for about 30 minutes. The officer said the search has detained more than 100 suspects.