The first attack occurred on Sunday morning west of Baghdad, killing one soldier and wounding another.
"Secondary explosions at the scene were from the cargo the
convoy was carrying," the military said in a statement.
Two hours later in the Iraqi capital, another car bomb exploded in the path of a convoy, killing one US soldier and injuring four others in the west of Baghdad.
"All five soldiers hit by the blast were medically evacuated to
a military treatment facility. One soldier died of wounds," the military said.
Thirteen Iraqis were killed in the Latifiya suburb in south-western Baghdad after a firefight with British troops.
At least 1129 US soldiers have
died in Iraq since March 2003
Medical sources told Aljazeera that clashes between British troops and Iraqis flared on Sunday evening. There were no immediate reports of British casualties.
Police sources said three of the Iraqis killed belong to the Supreme Council for Islamic Revolution.
British soldiers injured
A group headed by Jordanian Abu Musab al-Zarqawi claimed responsibility for a car bomb attack against a US convoy on the main road to Baghdad's international airport on Sunday.
The latest US deaths bring to 1129 the number of US troops
killed in Iraq since the US-led invasion in March 2003.
Meanwhile, two British soldiers have been injured near their post south of Baghdad.
The Ministry of Defence said on Sunday: "At 9.22 local time [0622 GMT] this morning, two British soldiers were injured in an incident in the vicinity of Camp Dogwood.They are being treated at an American hospital in Iraq."
A British military spokesman declined to give further details of the incident or of the soldiers' injuries.
The injuries follow the death of three British soldiers in a car bomb attack near Camp Dogwood on Thursday.
It was the first fatal attack on British forces since they moved closer to Baghdad to stand in for US forces in one of Iraq's most dangerous areas.
British forces are now working in
trouble spots around Baghdad
British troops had previously been serving only in the
relatively peaceful southern region of Basra.
But in a decision hotly debated in parliament, Prime Minister Tony Blair agreed earlier this month to dispatch 850 troops to volatile areas near the Iraqi capital to allow US troops to reinforce units fighting in Falluja and elsewhere.