KABUL, Afghanistan – More than 20 insurgents including Arab, Chechen and Pakistani fighters have been killed by NATO and Afghan forces who are ramping up operations in the east against a Taliban faction linked to al-Qaida, the international coalition said Saturday.

Separately, three more NATO troops — an American, a Briton and an Australian — died in separate insurgent attacks in the volatile south.

The joint force operation began Wednesday against insurgents holed up in a mountainous area of Paktia province. The operation focused on disrupting the Haqqani network’s movement in an area used to stage attacks in the capital, Kabul, and along a highway that links Khost province and Gardez, the provincial capital of Paktia, NATO said.

NATO officials had no further details about the death of the U.S. service member Saturday. But the Australian military said a member of the country’s elite Special Air Service Regiment was shot early Saturday in northern Kandahar province.

The British Ministry of Defense said Saturday that a British soldier serving with a mine-clearing unit died in a firefight the day before in Helmand province.