Two Afghan fighters also were killed and an unknown number injured in an operation, the Pentagon said.
CBS News Pentagon correspondent David Martin says this is the biggest U.S. ground operation of the Afghan war. Pentagon officals say it may go on for days, he adds.
The battle was taking place some 20 miles east of Gardez, the capital of Paktia province and near the Pakistan border.
“This mission involved Afghan and coalition service members, but the main effort is the Afghan forces,” the Defense Department said in a statement.
Not including the latest casualties, four members of the U.S. military had been killed in combat in the U.S.-led campaign that began Oct. 7. A CIA agent was killed during a prison riot while interrogating detainees.
It appeared the U.S.-backed Afghans made little headway on the first day of an offensive.
Afghan soldiers, who went into the battle aided by U.S. advisers and B-52 bombers, said in their initial assault they were forced to retreat under withering fire from 3,000 to 5,000 diehard fighters in bunkers on the snowy mountains.
They said there were a number of Arab and other foreign fighters among their foes.
“The fighting was very fierce and we had to pull back,” an Afghan soldier, who did not want to give his name, told Reuters.
Afghan forces broke off the attack in early afternoon and withdrew, possibly to allow U.S. bombers to soften up Taliban and al Qaeda positions overnight. Heavy bombers could be heard flying toward the area late Saturday.
In neighboring Pakistan, authorities sealed off the border along the mountains to block any fleeing Taliban or al Qaeda from escaping.
There was no indication whether bin Laden and Mullah Omar, both of whom Afghan officials say are still alive and on the run, were near the scene of the latest fighting.
Gardez, about 95 miles south of Kabul toward the Pakistan border, is seen as a likely hideout for the two leaders.
U.S. B-52 bombers have been out in force in recent days over Paktia province.
Even before word of the casualties, the new operation reinforced what the Pentagon long has maintained — that the war against terrorism in Afghanistan was far from over.
The battle plan called for a combination of American special forces and Army 101st Airborne assault troops fighting alongside Afghan allies on the ground with U.S. bombing support from the air, said Pentagon officials, speaking on condition of anonymity.
By way of comparison, big gains in the war from October through December came mostly in operations in which Afghan allies fought on the ground with small teams of U.S. special forces calling in bombing targets for warplanes.
The most recent and largest sustained bombing was in January, when warplanes bombed caves and exploded enemy weapons and ammunition for more than a week at Zawar Kili — where intelligence officials said al Qaeda — and Taliban were regrouping.
The new offensive opened near Gardez, in the eastern part of the country, and was backed by 60 American and 600 Afghans on the ground, Afghan officials said.
The last known ground operation was on Jan. 23 when U.S. special forces raided a compound where the U.S. mistakenly believed enemy figures were holed up. The Pentagon has said 16 people who turned out not to be to al Qaeda or Taliban were killed when they resisted.
Since then, there have been small unpublicized raids, said a U.S. defense official, speaking on condition of anonymity.
Coalition troops continue to gather intelligence on pockets of resistance, seizing material and interrogating people during these raids, the official said.
“We've said all along that it is not over ... in Afghanistan and that for some time there would be pockets of resistance,” Pentagon spokeswoman Victoria Clarke said Friday.
U.S. officials and Afghan sources estimate 4,000 to 5,000 foreigners who fought for the Taliban and al Qaeda remain inside Afghanistan. Many of them are believed to be in Paktia and other provinces along the Pakistan border.
Wives and children of al Qaeda , along with widows and families of al Qaeda dead, also are believed to be in hiding there.
They are receiving support from a variety of groups, including Kashmiri separatists, Islamic militants in Pakistan and some former officials of Pakistan's intelligence service, according to Afghan sources.
In Pakistan, a senior government official at the Pakistan border town of Miran Shah said Saturday that troops have blocked all routes to prevent escape of any al Qaeda and Taliban fleeing the attack.
The official, Javed Marwat, said a 60-mile strip with Afghanistan has been closed.
A tribal elder in the area, Haji Rasool Khan, said by telephone that his Madakhel tribe would not give shelter to any al Qaeda on the run.