"Talks with the Taliban have started... the talks are going on well," Karzai said, addressing a conference in Kabul.[break]
"Also foreign forces, especially the United States, are carrying out the talks themselves."
The US-led war in Afghanistan is in its 10th year and there are increasing calls for a political settlement to the conflict.
US Secretary of State Hillary Clinton earlier this year called on Taliban members to split from Al-Qaeda, renounce violence and accept the constitution so they can be reconciled to society.
The US embassy in Kabul did not immediately respond to a request for comment on Karzai´s remarks.
Western officials in Kabul stress that attempts to set up contacts with the Taliban are at a very early stage and that efforts are still being made to achieve a communication channel with the Taliban´s leadership.
Karzai last year set up a High Council for Peace featuring senior Afghan figures in a bid to pursue talks with the Taliban in return for them laying down their arms and accepting the constitution.
These have been rejected in public by the militants, who are leading a bloody insurgency against foreign troops and Afghan forces.
UN splits Al-Qaeda and Taliban on sanctions list
UNITED NATIONS: The UN Security Council has split the international sanctions regime for the Taliban and Al-Qaeda to encourage the Taliban to join reconciliation efforts in Afghanistan.
The council unanimously passed two resolutions on Friday, setting up one new blacklist of individuals and organizations accused of links to Al-Qaeda and a second for those linked to the Taliban militia.
The two groups have until now been handled by the same sanctions committee.
But the international powers wanted to separate them to highlight the divide between Al-Qaeda´s global jihadist agenda and the Taliban´s focus on Afghanistan.
The sanctions committee was set up in 1999 when Al-Qaeda had major bases in the Taliban, which ruled Afghanistan until they were driven out of power by US led forces.
The new resolutions, 1988 and 1989, send "a clear message to the Taliban that there is a future for those who separate from Al-Qaeda, renounce violence and abide by the Afghan constitution," said Susan Rice, UN envoy for the United States, which led the campaign for the division.
The United States welcomed the passage, saying it marked "a major step forward in the strengthening of the international sanctions regime against terrorists," said State Department spokesperson Victoria Nuland.
"The new regime will be an important tool to support the government of Afghanistan´s efforts to reconcile with insurgents who are willing cut ties to international terrorist organizations," she said in a statement.
Peter Wittig, Germany´s UN ambassador who heads the Security Council anti-terrorism sanctions committee, said the resolution sent "a strong signal of trust and support for the peace and reconciliation efforts of the government of Afghanistan."
US President Barack Obama has set July as the target date to start cutting the 100,000 American troops in Afghanistan and Defense Secretary Robert Gates said this month there could be talks with the Taliban before the end of the year.
The new sanctions regime for those who pose "a threat to the peace, stability and security of Afghanistan" gives the Afghan government a say in the listing and delisting of accused militants. An ombudsman also gets extra powers to recommend delistings.
The Security Council will have to vote unanimously to keep a person on a sanctions list if the ombudsman has recommended the name be taken off.
Wittig called the changes a "major advance."
While all 15 council measures backed the resolutions, India and Russia said there must be non easing up in the international fight against terrorism. "There must be no slackening of efforts to fight both Al-Qaeda and the Taliban," said Russian ambassador Vitaly Churkin.
Separately, the Security Council´s sanctions committee is considering taking about 20 former Taliban commanders off the UN blacklist.
The Afghan government had originally advanced about 50 names but withdrew many because it did not have the paperwork to back up the case, diplomats said. A decision on those still waiting will be taken in mid-July.
The remaining list includes five members of Afghan President Hamid Karzai´s Higher Council of Peace, which he set up last year to seek peace talks with Afghanistan´s former hardline rulers.
One of them, Mohammed Qalamuddin, was once head of the Taliban´s feared religious police.
There are 135 Taliban names facing sanctions. The 254 long Al-Qaeda list was cut by two this week following recommendations from an ombudsman.
One Sudanese-Canadian, Abousfian Abdelrazik, 49, went to the Security Council with a delegation of Canadian civic and labor groups in a bid to get his name taken off the Al-Qaeda list.
Abdelrazik has been on the UN list since 2006 and subject to an asset freeze and travel ban. Detained after travelling to Khartoum on what he said was a trip to see his ailing mother in 2003, he has denied any links to Al-Qaeda.
"Since my name has been on that list no one has given me any evidence about what I am supposed to have done wrong," he said after meeting sanctions committee officials in New York.
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