KABUL - Officials say a bomb placed on a bicycle in a busy market killed four people Sunday, including two children, while American fighter aircraft and ground forces killed 19 militants near the Pakistan border.

The bicycle bomb went off in Gereshk district of southern Helmand province. Doud Ahmadi, spokesman for the provincial governor, said a 10-year-old boy and an 8-year-old girl were among the victims. The Interior Ministry said it exploded in a market while people were shopping.

American fighter aircraft and U.S. and Afghan ground forces, meanwhile, killed the 19 militants in a rugged region of eastern Afghanistan along the border with Pakistan, the U.S.-led coalition said.

The fighting in Kunar province began Friday when militants attacked an Afghan-led combat patrol of elite commando forces, the coalition said. The U.S.-Afghan force returned fire and called for fighter aircraft, killing seven suspected militants.

Other militants repositioned on a ridge, and fighter aircraft killed 12 more, the coalition said in a statement late Saturday.

The coalition said no Afghan and coalition forces or civilians were wounded.

Violence is expected to rise in the coming months. President Barack Obama has ordered an additional 21,000 U.S. troops to join the 38,000 already in Afghanistan.

American special forces are helping train elite commandos as part of an overall U.S. effort to train the Afghan army so that U.S. and other NATO militaries can eventually withdraw.