With the insurgency at the most violent since the ouster of the Taleban in early 2002, despite the presence of tens of thousands of foreign troops, Western leaders say the conflict cannot be won militarily and talks must be held with some rebels.
Afghan officials said last week that Karzai met a senior delegation from Hezb-i-Islami, one of the three main groups fighting the government and foreign forces, his first confirmed talks with the group which in some ways rivals the Taleban.
Although the talks were preliminary, the public acknowledgement of the meeting was itself a milestone after many months of furtive efforts by Karzai to reach out to militants.
Qaribur Rahman Saeed, a member of the Hezb-i-Islami delegation, said the team had wrapped up its mission after meeting the president for a second time on Tuesday, and would now report back to fugitive leader Gulbuddin Hekmatyar.
"We are sending Mr. Karzai's viewpoints to our leader and will get his response on it after several weeks and then we will come to Kabul to resume a second round of talks," he said.
The group presented Karzai with a 15-point plan that includes a demand that Western troops begin pulling out from Afghanistan in July this year and withdraw completely within six months, although delegates have said the time-frame is negotiable.
"The draft plan may will be reformed. We are flexible. We want this process to continue and saw that feeling on the part of the government too. We are sure that there is sincerity on both sides," Saeed told Reuters.
Setting a firm time-table for the exit of foreign forces could also prompt the Taleban to join in the peace talks, he added.
US President Barack Obama plans to start withdrawing forces in July 2011, although the pace of the pace of the withdrawal will depend on conditions on the ground.
The Hezb-i-Islami talks come amid a bid by Karzai to reach out to insurgents that he hopes will eventually yield talks with the Taleban themselves.
Washington has been cautious, saying it backs Afghan efforts to reconcile with senior insurgents, but they must lay down their weapons and repudiate Al-Qaeda. US officials say talks with the Taleban themselves are unlikely to yield fruit until a "surge" of 30,000 extra troops this year yields gains on the battlefield.
"We're moving to a position of strength," the Chairman of the US Joint Chiefs of Staff, Admiral Mike Mullen, told reporters during a visit to Kabul on Wednesday when asked about the prospect of talks. "But I just don't think we're there yet."
On Tuesday, Karzai's chief spokesman Waheed Omer said the Hezb-i-Islami talks were making progress, but played down the chances of a quick breakthrough, saying he did not want to raise expectations and describing the contacts as in the early stage.
Hekmatyar, a former prime minister and the largest recipient of US aid during the war against the Soviet occupation in the 1980s, has shared some of the aims of the Taleban, but has led a separate insurgency, mainly in Afghanistan's east and north.
Hezb-i-Islami is not considered as big a threat by NATO forces as the Taleban or the network of followers of insurgent commander Jalaluddin Haqqani based mainly in the southeast.
