Two Taliban leaders killed in Afghanistan

(CNN) -- Local security forces and coalition soldiers killed two Taliban leaders and several other insurgents Thursday in western Afghanistan, NATO's International Security Assistance Force said.

Taliban leaders Haji Dawlat Khan and Haji Nasrullah Khan and a "significant number of other insurgents" were killed during "a successful operation against high-priority Taliban targets" in Herat province, according an ISAF statement.

The soldiers and local security forces also freed a number of men "handcuffed and imprisoned in appalling conditions" in a compound belonging to the insurgents, the ISAF said.

The rescued men are receiving medical care, and there was no evidence of civilian casualties in the operation, according to the ISAF.

The incident reflects increasing violence between troops and Taliban militants across Afghanistan and comes as U.S. commanders request more troops there.

Since May, the deaths of U.S. and allied troops have far outpaced such deaths in Iraq. As of Thursday, the toll in Afghanistan since May was 21 compared to seven in Iraq.

A soldier died Thursday of noncombat-related causes in southern Afghanistan, but the ISAF did not provide that soldier's nationality.

On Sunday, nine U.S. troops were killed in an attack on a combat outpost in eastern Afghanistan.

Two top Pentagon officials said Wednesday they expect to be able to recommend more troop reductions in Iraq this fall and will try to find ways to increase troops in Afghanistan.

One of the toughest fronts in the war has been the southern province of Helmand.

The British Defense Ministry said British troops in southern Afghanistan killed a senior Taliban leader on Saturday, the second such achievement in just over two weeks. The slaying of Mullah Bismullah Akhund happened in the Now Zad district of Helmand, long a Taliban bastion.

British troops, which are part of the ISAF, announced the killing on Thursday.

A Defense Ministry statement called Bismullah "a senior key facilitator and logistician responsible for the northern Helmand region."

The ministry said his death will disrupt the Taliban's leadership structure and hamper the group's ability to conduct attacks.

"He is believed to have commanded numerous fighters and was identified ... as a key player in the insurgency, and criminality, before the strike," according to the ISAF.

Saturday's operation happened 15 days after British troops killed another senior Taliban militant, Sadiqullah, in an Apache missile strike.

"Bismullah was closely associated with local Taliban leader Mullah Rahim, whose brother was also killed during this operation," ISAF said.

The Defense Ministry said that "combined with the elimination of Sadiqullah, this is the most significant blow struck against the Taliban logistics and facilitation chain in northern Helmand this year."

The U.S.-led coalition said it also is investigating an airstrike in western Afghanistan's Farah province. Launched after a coalition convoy was attacked Tuesday, it struck a house and killed eight civilians.

CNN's Joe Sterling contributed to this report

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