A soldier was captured by the Taliban on Tuesday in eastern Afghanistan, a Taliban commander confirmed to CBS News.

Neither the Army nor the Taliban will reveal the soldier's name or his unit.

"We are not providing further details to protect the soldier's well-being," Spokeswoman Capt. Elizabeth Mathias told the Associated Press.

An Afghan police official said the soldier went missing during the day Tuesday in the Mullakheil area of eastern Paktika province. Gen. Nabi Mullakheil said there is an American base in the area.

The news broke as thousands of U.S. Marines launched a major anti-Taliban offensive in southern Afghanistan. The missing soldier was not part of that operation.

CBS reported that the soldier was seized along with three Afghan citizens.

The Taliban commander, who spoke to [CBS News] via satellite telephone from the region, said a group of militants cornered the American soldier and his Afghan counterparts near a U.S. military base and took them hostage.

He said the captives' fate would be decided by Taliban leaders, but that the Islamic extremist group "would not mind an exchange of prisoners in this case."

The 10th Mountain Division, based at Fort Drum, has an extensive role in Afghanistan, but the military base nearest the capture, Forward Operating Base Orgun-E, is not home to a unit from the 10th Mountain Division, according to the security website GlobalSecurity.org