An Afghan child was shot dead in Monday during a gun battle between NATO and insurgent forces, and a US serviceman was killed in a bomb attack in the south of the country.
NATO did not provide further details on the death of the American.
Sunday's fighting in eastern Kunar province started when militants attacked a small US base in Watahpur district, according to Maj. Michael Johnson, a spokesman for the international military coalition.
Insurgents fired on the outpost and soldiers saw the rounds hit two children nearby, killing one and wounding the other, Johnson said.
Violence has risen in recent months along with a surge of US troops into Afghanistan. In July, a record 66 American service members were killed, compared with 44 in July last year. A record total of 103 international forces died in June, more than triple the figure for the same month in 2009.
Civilian deaths also have risen. The Afghan human rights commission released a report Sunday saying noncombatant casualties were up 6 percent to 1,325 for the first seven months of 2010 compared with the same period last year.
Elsewhere, the NATO command announced that a German unmanned surveillance aircraft crashed Monday in Kunduz province. The statement said the aircraft lost altitude due to technical problems and was destroyed on impact.