One soldier was killed by a homemade bomb. The improvised device was thrown at a US military vehicle during a late night patrol of the Kadhamiyah neighbourhood in the north of the capital.
Corporal Tod Pruden confirmed the attack took place at 1am.
Earlier, an Iraqi resistance fighter was shot dead in a separate incident after attacking an American military convoy and killing a US soldier.
"At 9:30pm last night, a First Armoured Division soldier was killed pursuing two Iraqi gunmen who were trying to ambush a patrol in the al-Azamiya neighbourhood.''
The three deaths follow the fatal shooting of a US soldier on Sunday in a cafeteria at Baghdad University, as attacks on the coalition forces continue to mount.
Since US President George Bush declared major combat over in Iraq, at least 72 US soldiers have died in guerrilla attacks, according to the US newspaper Arizona Republic.
The shootings followed a rocket-propelled grenade attack in the Iraqi town of al-Ramadi west of Baghdad on Sunday night, when snipers fired at a US patrol, according to witnesses.
Huge explosions were heard in the town located 100 km west of Baghdad, said the witnesses.
Civilians hit by US soldiers
Earlier, US troops shot dead two Iraqi civilians during clashes with guerrillas in al-Ramadi.
They said the occupation troops opened fire on a car carrying the two civilians after American vehicles were ambushed.
The shooting of civilians followed another incident in which four US soldiers were wounded after a rocket-propelled grenade attack in the same town.