Brig. Roger Lane said the troops were sent to eastern Paktia province after an Australian special forces patrol came under fire on Thursday. No coalition casualties were reported, but some enemy fighters were killed, Lane said.
Elements of the British 45 Commando group, "equipped with the full range of combat power," were sent by air and road to "close with the enemy and destroy them in an area historically used by the Taliban," Lane said.
He said a number of air attacks had already been launched.
"As before, the success of this operation will not be measured solely in terms of dead terrorists," he said.
"The first priority will be destruction or capture of the terrorists in the area, we will also aim to destroy enemy infrastructure that we may find," he said.
U.S. military spokesman Maj. Bryan Hilferty said the operation was taking place north of the eastern city of Khost.
He said American forces had not sent ground forces, but were backing the mission with U.S. Air Force AC-130 gunship airplanes and Chinook and AH-64 Apache attack helicopters.
In Australia, Brig. Mike Hannan said the first group of Australian troops came under heavy machine gunfire in hilly terrain Thursday afternoon.
A second group of soldiers trying to reach them also came under fire about four miles from the initial exchange, he said. They were able to fight their way through and join up with the help of U.S. air support. Hilferty said AC-130s were used.
The two units were then able to move to safety, Hannan said in Canberra.
No Australians were hurt, but at least one suspected enemy fighter was killed, he said.
About 150 Australian Special Air Service troops are in Afghanistan as part of the U.S.-led assault launched in October.
Lane said suspected al Qaeda or Taliban fighters had been behind the attack on the patrol. He declined to say how many enemy fighters there were, but said "it is clear that it is a substantial enemy force" and coalition forces, backed by a British artillery battery, had identified several enemy positions.
Lane said the fighting was taking place in a mountainous area at an altitude of 8,000 feet, but declined to be more specific. He said the mission could take days.
The U.S.-led coalition has been stepping up its search in eastern Afghanistan for al Qaeda and Taliban holdouts, who they say have dispersed into small groups and blended in with local residents or fled across the border to neighboring Pakistan.
Coalition troops had reported no enemy contact for weeks.
Also on Friday and in the same area, local security officials said that at least 10 Afghan tribesmen feuding over land were killed in eastern Afghanistan when U.S. planes bombed their positions after shooting erupted on the ground.
The shooting and subsequent bombardment took place after dark Thursday night, Khost security chief Sur Gul said.
He said two tribes, the Sabari and the Balkhiel, were skirmishing over ownership of a swath of trees that sit on a mountain near their villages about 30 miles north of Khost, a major town in eastern Afghanistan. Shooting erupted, Sur Gul said, and U.S. planes came along shortly afterward and began to drop bombs.
It was not immediately known whether the bombing was connected to the fighting reported by Lane. Hilferty said he was not aware of the bombings, but said Operation Condor was taking place in the same general area.
Sur Gul said at least 10 people were killed on both sides from the American bombardment. He had no information on injuries.
"We don't know why the U.S. planes fired," Sur Gul said.
An intelligence official in Khost, Chenar Gul, said some tribesmen shot in the air toward at least one U.S. plane passing overhead. He also reported "several" killed and injured.
The Afghan Islamic Press agency, quoting unidentified officials from Khost, gave a different reason for the deaths.
It said a marriage ceremony was taking place in Balkhiel on Thursday night, and men fired automatic rifles in the air as part of wedding tradition. Two U.S. helicopters were nearby, the news agency said, and U.S. planes arrived shortly thereafter and bombarded the area.
In recent months, U.S. planes have attacked positions, particularly in eastern Afghanistan, where Taliban and al Qaeda holdouts are believed to be hiding. Locals have complained of mistakenly targeted bombing campaigns that they say have killed innocents.
On Monday, British-led forces wrapped up a two-week search operation in eastern Afghanistan saying they had dealt a "significant blow" to al Qaeda's ability to mount future terrorist strikes by blowing up a huge of cache of ammunition located in several caves in Paktia province.
That operation involved about 1,000 British and Afghan troops and was backed by American air support and special operations soldiers.