The Taliban will meet United States representatives in two days to talk about making peace in Afghanistan.
The Taliban opened an office in Qatar, the capital of Doha, on Tuesday. It said it wants a political solution bringing about a just government and an end to foreign occupation.
However, US officials said the talks are on condition that the Taliban renounce violence, break ties with al-Qaeda and respect the Afghan constitution - including the rights of women and minorities.
NATO forces are still fighting the Taliban in Afghanistan, but NATO on Tuesday handed control of domestic combat operations for the whole country to the Afghan government.
President Hamid Karzai said Afghan forces will now lead all security activities.
Earlier, he said his government would also send a high-level delegation to talk to the Taliban.
But the Taliban has always refused to meet Mr Karzai or his government, dismissing him as an American puppet.
The BBC reports the level of trust between the Afghan government and the Taliban is described as "low".
US officials said prisoner exchanges would be one topic for discussion with the Taliban, but the first weeks will mainly be used to explore each other's agendas.
High Peace Council secretary Masoom Stanekzai told the BBC the talks would take place "within days".
"Eventually the talks should take place on Afghan soil. This is an Afghan issue. No-one other than Afghans can decide," he said.
But US officials stressed that this was the first step on a very long road, adding that there was no guarantee of success.
All foreign troops are expected to have left Afghanistan by the end of next year, but are now under the control of the Afghan government.
Fears of return to old ways
Radio New Zealand correspondent Jon Stephenson in Afghanistan says there is concern among the Afghan people that the withdrawal of foreign troops will lead the country back to its old ways.
He told Morning Report there was a general feeling of fear in Kabul last week and there's a strong sense that the attempt to stabilise Afghanistan and form some kind of uniform nation has failed.
Jon Stephenson said the feeling is that it is only a matter of time before people revert to old groups and a sort of civil war overtakes attempts to build a stable democratic nation.
He expects to see an increasing number of attacks by insurgent groups and said Afghan forces will have trouble stemming the tide.