More than 700 foreign troops have been killed in Afghanistan so far this year -- nearly a third of the total in over nine years of war.
While U.S.-led NATO forces have applied a surge strategy there is also a search on for ways to bring about a political solution as a countdown begins for the withdrawal of troops.
President Barack Obama has promised to begin pulling out U.S. forces in 2011, and NATO has agreed to end combat operations and hand security responsibility to the Afghan army by the end of 2014.
Speaking in Istanbul at the end of a trilateral summit between Turkey, Afghanistan and Pakistan, Karzai said "dignitaries" close to the Taliban had suggested Turkey could become a venue for talks if the Taliban were allowed to establish some kind of representation there.
"The idea of Turkey serving as a place where gatherings can take place, where representation can be established in order to facilitate reconstruction and reintegration has been discussed," Karzai told a joint news conference with his counterparts from Turkey and Pakistan.
"If Turkey can be kind enough to provide such a venue we, the government of Afghanistan, will be happy and pleased to see this facilitation take place."
Karzai had been asked to comment on an interview with a former Taliban official, Mullah Abdul Salam Zaeef by Britain's Daily Telegraph newspaper.
The proposal for the Taliban to be allowed to establish some kind of diplomatic presence in Turkey surfaced in the interview.
President Abdullah Gul of Turkey said he had not seen the report but voiced support in general terms.
"Whatever will serve the future reconstruction of Afghanistan -- we will be there," Gul said.
This was the fifth in a series of the trilateral summits held in Turkey, with the aim of building greater trust between Pakistan and Afghanistan.
Whereas Western government can tend to apply pressure in dealings with the Afghan and Pakistani governments, Turkey is able to operate at a different level diplomatically, being a fellow Muslim country with historically warm ties with both.
Turkey has troops serving in non-combat roles with NATO forces in Afghanistan, and also has well established military-to-military contacts with Pakistan.
The Afghan and Pakistani militaries are cooperating with NATO forces to fight the Taliban and Islamist militants who run with al Qaeda.
But according to some analysts, Afghan and Pakistani intelligence agencies suspect each other of secretly encouraging militant factions to launch attacks to destabilize each other's governments in the hope of winning greater influence once Western forces leave the region.
Pakistan's President Asif Ali Zardari denied that the Pakistan military's Inter-Services Intelligence was supporting the Taliban, but said there were "non-state actors" who were helping the militants.
"Let me assure you that the ISI is not involved with the Taliban," Zardari said.
Gul stressed the need for the intelligence services to work together and a statement issued at the end of the summit said the heads of three countries' intelligence agencies had met in Istanbul on December 2-3.
ISTANBUL (Reuters) - By Simon Cameron-Moore (Editing by Angus MacSwan)