The latests incidents bring American combat deaths in the country this year to 51, the bloodiest period for US forces since the fall of the Taliban.
One US soldier died during a “ground assault operation” by Afghan and US forces west of the southern city of Kandahar on Monday, when armed fighters fired rocket-propelled grenades and small-arms fire at their vehicles, the US military said in a statement.
Another US soldier was wounded.
The coalition forces returned fire, killing two fighters and wounding a third.
In a separate incident, a US forward operating base near the eastern city of Asadabad came under mortar, rocket-propelled grenade and small-arms fire on Monday, the statement said.
One US Marine was killed in that attack.
Karzai believes there is no
The latest casualties came despite post-election comments from Afghan President Hamid Karzai calling for a change in strategy in the war against the Taliban rebels.
Karzai said he did not think there was a big need for military action any more, and questioned the use of US air strikes, some of which have caused civilian casualties.
US defence officials have said that while they agree with Karzai on air strikes, they still see the need for military action.
The Taliban vowed last week to step up its rebellion after failing to derail the election.
US President George Bush’s national security adviser Stephen Hadley said in Kabul on Monday that there was no quick fix for the problem of what he called militancy and much closer cooperation was needed between Afghanistan, neighbouring Pakistan and Washington.