A delegation from a powerful Afghan militant group has met officials for talks in Kabul, the government says.
The team from the Hezb-e-Islami group of Gulbuddin Hekmatyar held talks with president Karzai, his spokesmen said.
It is the first confirmed direct contact between Mr Karzai and envoys of Mr Hekmatyar, who is wanted by the US.
Hezb-e-Islami fighters are based mainly in eastern Afghanistan and share many aims with the Taliban. The two groups clashed in the north in recent months.
Observers say the talks in Kabul may only be preliminary but they come at a fluid time in Afghan politics, with a peace jirga or tribal gathering due to be held in a few weeks' time and a surge in US-led troop numbers under way.
On Friday the former UN envoy to Afghanistan Kai Eide confirmed he had been holding secret contacts with top Taliban leaders for the past year.
Speaking to the BBC, Mr Eide strongly criticised pakistan's recent arrests of high-ranking Afghan Taliban leaders, saying they had put a stop to the contacts.
The Hezb-e-Islami delegation is headed by a former Afghan prime minister, Qutbuddin Helal, who is deputy to Gulbuddin Hekmatyar, another former prime minister.
I can confirm that a delegation of Hezb-i-Islami... is in Kabul with a plan, Reuters news agency quoted a spokesman for Mr Karzai as saying.
Among the group's reported demands are a pull-out of foreign forces from Afghanistan by this summer, a year ahead of a date indicated by US president Barack Obama for any withdrawal to begin.
They also want fresh elections within a year and a new constitution.
The main condition is the empowerment of president Karzai to engage in talks and make decisions, a spokesman for Hekmatyar, Wali Ullah, said.
The aggressive occupying forces should also announce a schedule for leaving Afghanistan.
Clashes with Taliban
Mr Hekmatayar is a highly controversial figure.
His group has battled Nato and Afghan forces in Afghanistan's east and north for years, while the Taliban have led the insurgency in the south.
Earlier this month, officials said that at least 60 militants were killed in fighting between the Taliban and Hezb-e-Islami in Baghlan province in northern Afghanistan.
Reports said they had clashed over control of local villages and taxes.
The two groups have previously been allied in their opposition to Afghanistan's central government and the presence of foreign forces.
Along with the Taliban, Hezb-e-Islami has been blamed for much of the insurgent violence in Afghanistan.
Mr Hekmatyar has previously offered to negotiate with the government - on the condition that foreign forces leave the country.
He was one of the main recipients of US military aid during the Soviet invasion of Afghanistan in the 1980s, but was later vilified for his part in the fighting among mujahideen factions which killed more than 25,000 civilians in the early 1990s.
He was designated a terrorist by the United States in 2003 for supporting al-Qaeda.