Late on Saturday, troops backed by air strikes attacked two areas close to the Sangin district of Helmand province.
The raids were part of a major offensive launched last month by foreign troops in response to a wave of violence by a resurgent Taliban across the south.
Nabi Mullahkhail, Helmand’s police chief, said: “Twenty-seven Taliban were killed in one of the attacks in which coalition and Afghan forces took part and eight other Taliban died in another raid.”
He said that one of those killed was a local Taliban commander.
There were no reports of casualties among coalition or Afghan troops.
Another 10 Taliban fighters were killed on Saturday in an early morning air assault in Sangin.
The coalition said they had taken control of Sangin, an opium-growing district, from the Taliban in the offensive.
A coalition soldier died of wounds suffered during a fire fight on Sunday in the southern province of Zabul, the US military has said.
The soldier’s nationality was not released.
In a separate incident, a suicide bomber blew himself up in front of a government building in the southeastern town of Gardez on Sunday, killing four and wounding at least 23.
In the western Herat province, a roadside bomb blast killed six Afghan soldiers and wounded three others as they patrolled with coalition forces on Sunday.
The recent coalition strikes in Afghanistan are part of a joint operation between British, US and Canadian troops.
There have been claims that civilians have been killed in the strikes and Hamid Karzai, the Afghan president, has ordered an investigation into reports that civilians were killed in a coalition air attack in the Uruzgan province on Monday.
The US military said that there had been no reports of civilian deaths and Major Tom Collins, the coalition spokesman, said that the claims had been fabricated as part of a “propaganda campaign”.