"As you said, Mr. Chairman, there is no military solution here, so as General Petraeus and General McChrystal said, you cannot win this war by killing every member of Taliban," Holbrooke, told US senators on Wednesday, Press TV reported.
He made the remarks as casualties of US-led troops rise in Afghanistan; more than 350 foreign soldiers have been killed in Afghanistan since the beginning of this year.
Meanwhile, Holbrooke defended the Obama administration's decision to push more US troops into Afghanistan, but noted that July 2011 is a deadline for starting a withdrawal of soldiers from the war-torn country.
"The idea here was quite clear: to tell the world and the Afghans that we do not have an open-ended, limitless, Vietnam-type escalation," Holbrooke said.
"The size, scope, timing, pace and an end-point for combat troop presence has not been decided on," AFP quoted the envoy as saying Wednesday.
"I do not want to give an optimism/pessimism report to you... I think there are significant elements of movement forward in many areas but I do not yet see a definitive turning point in any direction," he further explained.
Some 140,000 US-led troops are currently stationed in Afghanistan. A further 10,000 are expected to be deployed there in the coming weeks.
NATO's mounting death toll has caused public support to plummet for the Afghan war across Europe and the United States.
Meanwhile, results of a CBS poll show most Americans believe the war in Afghanistan is a no-win scenario.
According to the poll, 60 percent of American people think the Afghan war is being handled badly. Fifty-one percent of Americans want the US government to set a date for the withdrawal of troops from Afghanistan.