One of the soldiers died when a convoy was hit by an explosion about 30 miles northeast of the capital, Baghdad. Four others were wounded.
Another soldier was killed, and one wounded, in a roadside bomb attack in the centre of the city.
Earlier, the US Administrator in Iraq, Paul Bremer, said the US was open to new ideas on the handover of power to Iraqis.
Speaking in a televised interview, Mr Bremer said the US was committed to handing over power to an Iraqi administration in June.
But he said they would wait to hear the report of the UN envoy to Iraq, Lakhdar Brahimi, about the feasibility of holding elections, before they pushed ahead with their plans.
