BAGHDAD (Reuters) - Two U.S. soldiers were killed and nine wounded on Tuesday when a gunman in Iraqi army uniform attacked them at an Iraqi base, U.S. officials said a week after Washington declared a formal end to U.S. combat operations.

The soldiers were part of a security detail for a U.S. company commander who was meeting members of Iraq's security forces at a commando compound near the city of Tuz Khurmato, 170 km north of Baghdad, a U.S. military statement said.

The assailant was shot and killed, the statement said.

"Initial reports indicate 11 U.S. soldiers were engaged with small arms fire, killing two and wounding nine," the statement said.

They were the first American soldiers killed since U.S. forces formally ended combat operations in Iraq a week ago, more than seven years after the invasion that ousted dictator Saddam Hussein.

Iraqi soldiers and police have been largely responsible for security in Iraq for months.

"This is a tragic and cowardly act, which I firmly believe was an isolated incident and is certainly not reflective of the Iraqi security forces," Major General Tony Cucolo said in the U.S. statement.

The gunfight resulted from an argument between an Iraqi soldier and U.S. personnel during a training session run by the Americans, according to Iraqi police and military sources.

Nearly 50,000 American troops remain in Iraq to train and assist the Iraqi military. But U.S. forces opened fire and provided air support for Iraqi forces during an attack on an Iraqi army base in Baghdad on Sunday.

Violence has declined sharply in Iraq since the peak of sectarian warfare in 2006-07 but insurgents continue to launch attacks daily, many targeting Iraqi soldiers and police.

The failure of political leaders to form a new government six months after a parliamentary election has stoked tensions.

(Reporting by Jim Loney in Baghdad, Sabah al-Bazi in Tikrit and Mustafa Mahmoud in Kirkuk; Editing by Andrew Roche)