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"This breaks our heart," Gates said at a news conference at the start of a two-day visit in which he will travel to southern and eastern provinces that have formed the main zone of fighting between U.S.-led forces and Taliban guerrillas, Defense Department spokesman Geoff Morrell said.
Gates' visit comes six days after U.S. helicopter crews killed nine boys cutting firewood on a forested mountainside in the Pech valley area of Kunar province in eastern Afghanistan after mistaking them for Taliban.
Hundreds of Afghans marched to protest civilian deaths and, on Sunday, Karzai rebuffed an expression of regret for the boys' deaths by the U.S. commander in Afghanistan, Gen. David Petraeus.
NATO has also apologized for the mistaken killings.
"President Karzai said that only regret is not sufficient and also mentioned that civilian casualties during military operations by coalition forces is the main reason for tension in relations between Afghanistan and United States," his office's statement said. "It is not acceptable for the Afghan people anymore. Regrets and condemnations of the incident cannot heal the wounds of the people."
Lt. Gen. David Rodriguez, who directs day-to-day operations of coalition forces across Afghanistan, issued a video statement of apology later. In the video, Rodriguez said troops at a base in the valley were responding to a rocket attack and dispatched attack helicopters to the location they were told the rockets came from. He said the helicopters thought they were engaging insurgents.
Gates said the United States is beginning to decide what its responsibilities will be in Afghanistan after U.S. combat troops leave. He ruled out permanent military bases.
Karzai wants U.S. military support even as he heavily criticizes the U.S.-led military campaign for being too quick on the trigger.
Gates said the United States is interested in keeping a military presence beyond the planned end of combat in three years. At a news conference with Karzai, he said a team of U.S. officials would arrive next week to begin negotiations over a new compact for U.S.-Afghan security relations after 2014, when all international combat forces are supposed to be gone. U.S. forces have been in Afghanistan since 2001, and President Barack Obama has repeatedly said the war is not open-ended.
Gates' promise to draft a post-2014 "strategic partnership" with the poor, unstable nation is meant to reassure the mercurial Karzai, who fears that he and the fragile civilian government might be overthrown without U.S. military backing.