Karzai last year rolled out a reintegration and reconciliation plan that called on moderate members of the Taliban to join the political process in exchange for pledges of peace.
Mohammad Masoom Stanekzai, secretary of an Afghan peace council and security adviser to the president, said both sides have discussed reconciliation.
"We're in touch, we talk all the time, we've done a lot, we've sent representatives to their sides and they've sent representatives to our side," he was quoted by The New York Times as saying.
Taliban spokesmen in Afghanistan deny they are embracing a reconciliation plan, stressing they won't talk while foreign military forces are in the country. Stanekzai said the Taliban won't confirm the negotiations for "political reasons."
Karl Eikenberry, the U.S. envoy to Afghanistan, said Washington supported Karzai's plans to bring in moderate Taliban members.
"We are all 100 percent behind reintegration and reconciliation," he told the Times.
Karzai is encouraging a review of the names on a terrorism blacklist represented by U.N. Security Council Resolution 1267. Removal, he says, will facilitate reconciliation.