Five militia troops contracted to the US-led coalition and an Afghan soldier also died in attacks.
The Taliban has apparently claimed responsibility for the bomb blast.
The US troops were on patrol with the
Afghan army when their Humvee vehicle hit a suspected improvised explosive device, the coalition said in a statement.
"Shortly after the attack, the patrol was engaged with small arms and rocket-propelled grenade fire.
"The coalition responded with fixed- and rotary-wing attack aircraft to support the US forces on the ground," it said.
Three other US soldiers have died in Afghanistan this year, two of them in hostile fire.
In other violence, five Afghan militiamen contracted to the coalition were killed late on Sunday in an ambush by suspected Taliban fighters in the troubled Helmand province, police said.
Two were killed outright, the bodies of three were discovered later and two survived, provincial police chief Abdurahman Saber told AFP.
A purported spokesman for the ousted Taliban regime, Qari Yousuf Ahmadi, also claimed responsibility for the attack in Helmand's Girishk district and said eight soldiers had been killed.
Helmand is the country's top opium-producing area, and is the scene of regular clashes.
More than 40 people were killed there earlier this month in a single day of battles between suspected Taliban and security forces.
In the restive province of Kunar, an Afghan soldier was killed and five others wounded when a roadside bomb ripped through their vehicle, police said.
Provincial police chief Mohammad Hassan Farahi blamed the attack on the "enemies of Afghanistan", a term often used to refer to remnants of the Taliban, their Al-Qaeda allies and other Islamist groups.
Taliban and other militants have for four years been carrying out regular guerrilla-style attacks in Afghanistan, hindering its attempts to stabilise and rebuild after 25 years of war.