Two suicide car bombers killed only themselves in an attack on U.S. forces Wednesday, while a U.S.-led coalition soldier died in a land mine explosion and 12 Taliban militants were killed in a raid on their compound, officials said.

Secretary of State Condoleezza Rice acknowledged a rise in violence on a visit to Kabul but promised victory over resurgent Taliban fighters.

The coalition soldier was killed and three were wounded in the Nawzad district of Helmand province, the military said. Their nationalities were not released, but British and American forces make up the majority of troops in Helmand.

The coalition patrol was conducting security operations when the armored vehicle struck a land mine that the coalition said was likely left behind from previous conflicts and not planted by Taliban militants.

CountryWatch: Afghanistan

Three men were involved in planning the suicide attack in southern Afghanistan's Zabul province, although only two were inside the vehicle that blew up near a U.S. convoy just outside the provincial capital of Qalat, said police chief Noor Mohammed Paktin.

No civilians or coalition soldiers were wounded, said Ali Khail, spokesman for the provincial governor.

A purported Taliban commander, Mullah Masum, claimed responsibility for the suicide bombing targeting the U.S. convoy. But he mentioned only one Taliban fighter was involved. His claim could not be verified.

Masum promised there would be more attacks in the future, saying: "We will pursue suicide attacks against coalition forces." He also warned local Afghans to stay away from coalition forces because militants would launch more attacks.

Coalition and Afghan troops raided a compound in a village in Shahidi Hassas district of Uruzgan province, killing 12 Taliban militants hiding there, the coalition said. The targeted compound was frequently used by militants as a meeting place, the military said.

Another attack near northern Kunduz province left three German soldiers slightly wounded Wednesday, the German military said.

Militants shot at a patrol of two German armored vehicles, and troops returned fire, Germany's military command center said. It was the second time in two days that German soldiers had come under attack in the region.

The violence comes as more than 10,000 U.S.-led forces hunt resurgent militants across southern Afghanistan. Bombings and ambushes targeting coalition and Afghan forces are on the rise more than four years after the invasion that toppled the Taliban regime.

Rice, on a visit to the capital, acknowledged that the recent spike in violence is a concern for the United States and the American-backed government of President Hamid Karzai, but she promised victory over Taliban militants.

Rice said the United States is committed to Afghanistan for the long haul and called Karzai one of the world's most respected leaders.

The Afghan president said optimism about his country's gains does not mean he is blind to its challenges, among them corruption and the drug trade. Afghanistan produced more than 4,500 tons of opium last year, about 90 percent of global supply.

Militants are waging their deadliest campaign in Afghanistan since the Taliban's 2001 ouster. More than 600 people, mostly militants, have been killed since mid-May. Afghan officials say the Taliban is making an all-out push to scare Britain, Canada, the Netherlands and Romania from deploying some 6,000 NATO-led troops in southern Afghanistan.