(CNN) -- Local security forces and coalition soldiers in western Afghanistan killed several insurgents Thursday in what the NATO command called a "successful operation against high-priority Taliban targets."

British troops detain suspected Taliban Militants during a recent operation in Afghanistan.

The operation took place in the Shindand district of Herat province. Two Taliban leaders, Haji Dawlat Khan and Haji Nasrullah Khan, and "significant number of other insurgents" were killed, according to a statement from NATO's International Security Assistance Force.

It added there was no evidence of civilian casualties or accidental damage in the operation, in which a "number of men were discovered handcuffed and imprisoned in appalling conditions in one of the insurgent compounds."

The incident reflects the increasing violence between troops and Taliban militants across Afghanistan and the growing concern in the United States that the war there should be more of a priority than it has been.

Since May, the deaths of U.S. and allied troops have far outpaced the toll in Iraq. On Thursday, the toll in Afghanistan was 21 compared to six in Iraq. The International Security Assistance Force did not provide the nationality of the soldier who died in Afghanistan Thursday.

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 its troops in southern Afghanistan killed a senior Taliban leader, two weeks after another leading militant died in a British missile attack.

Mullah Bismullah Akhund was killed Saturday in the Now Zad district of Helmand, long a Taliban bastion.

The Defense Ministry, in a statement on Wednesday, called Bismullah "a senior key facilitator and logistician responsible for the northern Helmand region." The ministry says 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 by Task Force Helmand as a key player in the insurgency, and criminality, before the strike," according to ISAF.

British troops, which are part of the assistance force, announced the killing on Thursday. Saturday's operation occurred 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.
What did NAATO say? Who is described to be a senior key facilitator? Who killed another Taliban leader? Who was attacked? What did the UK say? What international organization reported on these events? Who said its troops killed another senior Taliban leader? Number of Taliban leaders killed? Who is described as a "senior key facilitator and logistician?
the NATO command called a "successful operation against high-priority Taliban targets." Mullah Bismullah Akhund British troops coalition convoy "successful operation against high-priority Taliban targets." NATO's NATO's International Security Assistance Force. Two Mullah Bismullah Akhund
question: What did NAATO say?, answer: the NATO command called a "successful operation against high-priority Taliban targets." | question: Who is described to be a senior key facilitator?, answer: Mullah Bismullah Akhund | question: Who killed another Taliban leader?, answer: British troops | question: Who was attacked?, answer: coalition convoy | question: What did the UK say?, answer: "successful operation against high-priority Taliban targets." | question: What international organization reported on these events?, answer: NATO's | question: Who said its troops killed another senior Taliban leader?, answer: NATO's International Security Assistance Force. | question: Number of Taliban leaders killed?, answer: Two | question: Who is described as a "senior key facilitator and logistician?, answer: Mullah Bismullah Akhund