US Marines and British troops under Nato command launched an operation in Garmser two weeks ago, saying they aimed to drive out the Taliban and destroy their support networks.
A separate air strike on Monday by Nato's International Security Assistance Force killed four Taliban fighters, including a local commander in the eastern province of Paktia which also borders Pakistan, an Afghan army spokesman said.
Thousands displaced
The air raid was called in after troops received intelligence about a Taliban meeting in the area, Mastak Khan, the force's spokesman, told the AFP news agency.
The Afghan government said on Monday that the fighting, including air strikes, had forced about 6,000 people to leave their homes in Garmser.
Gulab Mangal, governor of the Afghan province of Helmand, said at least 150 Taliban and foreign fighters were killed in Garmser district, according to an Al Jazeera correspondent in Afghanistan.
Eyewitnesses told Al Jazeera that a number of Nato military vehicles had been destroyed in Grishk district in Helmand.
Taliban fighters shot down on Monday night a Nato helicopter in Kamdesh district in Nuristan province, Al Jazeera's correspondent quoted Dhabihullah Mujahid, spokesman for Taliban movement, as saying.
Nato forces refused to comment on the Taliban’s statement.
The US military says Garmser is a gateway into Afghanistan from Pakistan where fighters are said to have bases.