Baghdad, Iraq (CNN) -- An Iraqi soldier opened fire Tuesday on a group of U.S. soldiers in northern Iraq, killing two and wounding nine others, the U.S. military and the Iraqi military said.
They are the first American deaths in Iraq since the U.S. combat mission officially ended last week.
The attack occurred inside an Iraqi army commando compound when the soldier, clad in an Iraqi army uniform, fired on the U.S. soldiers near the Salaheddin province city of Tuz, the U.S. military said. The attacker was shot and killed.
Maj. Gen. Mohammed al-Askari, a Defense Ministry spokesman, identified the shooter as Soran Rahman, from the Iraqi army's 4th Division.
Al-Askari said Rahman got into a fight with U.S. soldiers, and then pulled his weapon and fired on them before he was shot dead. The spokesman said a joint U.S.-Iraqi investigation into the incident was under way.
The soldiers were part of a security element for a U.S. company commander who was meeting with members of Iraqi security forces at the compound.
"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" in Salaheddin, said Maj. Gen. Tony Cucolo, commander, Task Force Marne.
In a second attack in Salaheddin province, a U.S. soldier and a number of Iraqis were wounded when a convoy in central Tikrit was hit by grenades early Tuesday afternoon, a U.S. military spokesman said. Soldiers who were in the vehicle that was attacked killed the grenade thrower, he said.
An Iraqi Interior Ministry official and police in Tikrit said that the man threw two grenades at the convoy, damaging a vehicle, and that U.S. forces then opened fire "randomly," killing a civilian and wounding four others.
But a spokesman for the U.S. military issued a statement disagreeing with that assessment, saying the U.S. military believes that the civilians' wounds were caused by the grenade that exploded and not from indiscriminate gunfire.
He said a U.S. military investigation concluded that the civilians' wounds were caused by shrapnel and not from bullets.
Two witnesses identified the body as that of the attacker, the spokesman said.
More than 4,400 U.S. troops died in Iraq during the war. While violence has dropped in the last two years, President Barack Obama said last week that "violence will not end with our combat mission."
"Extremists will continue to set off bombs, attack Iraqi civilians and try to spark sectarian strife. But ultimately, these terrorists will fail to achieve their goals," he said in a speech from the Oval Office on August 31.
That's when he announced the end of the U.S. combat mission and the beginning of a new American phase in Iraq.
U.S. troops are expected to advise and assist Iraq's security forces, back Iraqi troops in counterterrorism missions and protect American civilians there during a transitional period.
Unless the United States and Iraq forge a new agreement, all U.S. troops are scheduled to depart Iraq by the end of 2011.
CNN's Arwa Damon contributed to this story.