A bomb killed two American soldiers and wounded three others Thursday in southern Afghanistan, the U.S. military said Saturday, and an attack in an eastern province killed three children and a policeman on the first day of the Islamic holy month of Ramadan.

The attacks in the wake of a historic presidential election this month were a reminder of the insecurity that threatens Afghanistan's nascent democratic experiment three years after the fall of the Taliban.

Ballot counting from the vote gathered speed after a one-day break, and the interim president, Hamid Karzai, streaked ahead of his rivals in early returns. Karzai, the U.S.-backed favorite, had 71 percent of the vote with 4 percent of the ballots counted.

The U.S. military said a homemade bomb hit an American Humvee on patrol in the southern province of Uruzgan on Thursday, killing two soldiers and wounding three others, one of them critically.

Karzai condemned a separate assault Friday in eastern Konar province in which a truck was set on fire and then a remote-controlled bomb detonated, killing the three children and a policeman. He described it as a terrorist atrocity committed by "enemies of Islam."

On Saturday evening, four rockets also landed in the capital, Kabul. Three struck houses near the airport, injuring one woman, police and residents said.

While election day, Oct. 9, was mostly peaceful despite threats by Taliban-led rebels to sabotage the vote, their insurgency still simmers, particularly in the country's lawless south and east. About 1,000 people, many of them insurgents, have died in political violence so far this year.

About 2,500 election staff resumed work Saturday morning at eight counting centers across Afghanistan after a day off to mark the start of Ramadan.

Final results are expected at the end of October, although it should be clear within days who has won -- and whether the victor has secured the majority needed to avoid a runoff.