KABUL, Afghanistan -- Afghan President Hamid Karzai confirmed his government has been in informal talks with the Taliban on securing peace in war-weary Afghanistan "for quite some time" -- the latest in a series of high-level acknowledgments of contacts with the insurgent group.

The comments came as Taliban fighters ambushed a military supply convoy in the east Monday and fought with Afghan forces in the south.

Unofficial discussions have been held with Taliban representatives over an extended period, Karzai told CNN's "Larry King Live" in an interview to be broadcast Monday.

"We have been talking to the Taliban as countryman to countryman," Karzai said. "Not as a regular official contact with the Taliban with a fixed address, but rather unofficial personal contacts have been going on for quite some time."

Afghan presidential spokesman Waheed Omar said it was not the first time Karzai had acknowledged talks, saying both the president and his office have repeatedly confirmed unofficial discussions.

"He has talked about it in the past as well. It's not hidden from anyone," Omar said. The president's office previously confirmed there were informal talks with different levels of Afghan Taliban over the past couple of years.

"We have said that there have been contacts in the past, initiated sometimes by the government, sometimes by the armed opposition," Omar said. He said these have been through intermediaries.

NATO's top commander in Afghanistan -- Gen. David Petraeus -- has also said the military coalition was aware of overtures made by Taliban insurgents at the highest levels to the Afghan government.

The drumbeat about talks comes as support for a drawn-out military push in Afghanistan is waning in the United States and with other NATO allies as the war enters its 10th year. Sending thousands more U.S. troops this summer to the country's south has yet to show significantly increased security in the Taliban heartland and violence has risen countrywide in recent months.

In the east on Monday, Taliban fighters ambushed a supply convoy guarded by Afghan military contractors as it traveled through Ghazni province on its way to Kandahar in the south, said provincial chief of police Zarawar Zahid. An hourlong gunbattle killed eight insurgents and wounded two Afghan security contractors in Qarabagh district.

Six militants died in operations by Afghan forces Sunday in southern Helmand province's Marjah and Greshk districts, the Defense Ministry said in a statement issued Monday.

The Afghan government says it hopes to make talks more structured with a "peace council" that will aim for formal talks with insurgent groups. On Sunday, former President Burhanuddin Rabbani was named chief of the council. Rabbani was one of a group of mujahedeen leaders who fought the Soviets in the 1980s. He was Afghanistan's president between 1992 and 1996, when he was ousted by the Taliban.

Omar said the panel, which formally began work Thursday, should become the conduit for formal talks.

"We hope that the signals that have been sent from the different representatives of the Taliban, and the kind of contact, direct and indirect, from the past will materialize into substantive talks led by the High Council of Peace," Omar said.

Publicly, the Taliban have said they won't negotiate until foreign troops leave the country, yet many Taliban leaders have reached out directly or indirectly to the highest levels of the Afghan government.

Last February, Karzai sent a small delegation of former Taliban members to Saudi Arabia to seek the kingdom's help in kick-starting talks with the Taliban. But Saudi Foreign Minister Prince Saud al-Faisal said the kingdom would not get involved in peacemaking unless the Taliban severed all ties with bin Laden and his al-Qaida terror network -- a key U.S. demand.

One of the former Taliban members, Abdul Salam Zaeef, said unequivocally then that he could not negotiate on behalf of the Taliban. The meeting ended without any results.