The two paratroops from the Fourth Brigade Combat Team, 82d Airborne Division, disappeared Wednesday during a routine resupply mission, the military said in a statement.

The military provided no further details on the disappearance, and neither NATO nor Afghan officials immediately explained how their forces got into the firefight, nor did they provide a breakdown of the casualties.

Such disappearances are rare.

The last time an American service member went missing in Afghanistan was in June, when Pfc. Bowe R. Bergdahl was captured after straying from a U.S. base near the eastern border with Pakistan.

On July 18, Taliban insurgents released a video of the 23-year-old soldier from Idaho.

U.S. military officials have said little about the search for Bergdahl for safety reasons, and it is unclear whether he is being held in Afghanistan or Pakistan.

Afghan officials indicated it was unlikely that the two other missing Americans had been captured.

The Afghan western regional police chief, Ikram Uddin Yawar, said a helicopter with NATO had been dropping food supplies in the Bala Murghab district of Badghis province when some of the boxes ended up in a river. He said the two missing soldiers were swept away by strong currents when they tried to retrieve the food.

U.S. and NATO officials would not verify the account while the search was under way.

"We are doing everything we can to find them," said Navy Capt. Jane Campbell, a spokeswoman for the coalition.

"The families of these service members have been notified about their loved ones' status, and we will continue to keep them informed as information becomes available."

The 82d Airborne Division is based at Fort Bragg in North Carolina.

Qari Yousef Ahmadi, a Taliban spokesman reached by telephone, said insurgents ambushed the joint forces in the same district where the soldiers went missing. He said three Taliban insurgents were killed in the clash.

Also yesterday, the NATO force announced the deaths of three service members Thursday in two bombings in southern Afghanistan. The dead included two Americans, the military said.

Last month was the deadliest of the eight-year war for U.S. forces, with 59 service members killed.

A key U.S. ally, Canada, meanwhile, announced its military leaders had begun preparations for its 2,800 troops to leave Afghanistan in the summer of 2011, the Associated Press reported.

Prime Minister Stephen Harper's government has said it will not extend Canada's military mission even if President Obama asks.

Another major ally, Britain, warned it would withdraw support - and not send additional troops - unless the Afghan government of President Hamid Karzai cracked down on corruption.

"I am not prepared to put the lives of British men and women in harm's way for a government that does not stand up against corruption," Prime Minister Gordon Brown said, reflecting public outrage over growing troop casualties.