Hamid Karzai, the Afghan president, seems likely to win support from a national peace conference for his plan to negotiate a deal with the Taliban.
The Taliban did not participate in the conference, or jirga, to discuss the country's future, held in Kabul, the Afghan capital, and attended by 1,500 tribal elders, religious leaders and other notables.
Details for specifics of any peace plan, which would give rank-and-file Taliban fighters incentives to lay down their arms, were not forthcoming.
Karzai, whose political standing has been hurt by allegations of electoral fraud, a deteriorating security situation and government corruption, hopes backing from the jirga will lend legitimacy to his government.
"Everybody agrees with peace and peace without negotiations is not possible," Hamid Gailani, a powerful politician from the Taliban's heartland in the province of Kandahar, said on Thursday at the end of a closed-door meeting.
The Taliban has dismissed the jirga as a "phony reconciliation process". They insist that there can be no negotiations until all foreign troops leave Afghanistan.
Qiamuddin Kashaf, the jirga's deputy chairman, said there was support among delegates for a new ministry or commission that could push forward the reconciliation process.
Al Jazeera's James Bays, reporting from Kabul on Friday, said many of the proposals reached by the jirga will "please the Afghan government and the international committee.
"But other proposals - such as the release of Taliban prisoners, closure of Guantanamo, Bagram and other jails, a timetable for the withdrawal of international troops - will cause some considerable alarm if they make into the final declaration of this jirga".
Delegates, who were divided into 28 sub-committees with about 50 people sitting on each committee during meetings on Thursday, fiercely debated whether anti-government leaders should be removed from the United Nations blacklist that freezes assets and bars overseas travel.
Others wanted US bounties on the heads of senior Taliban leaders to be lifted.
"We think some Taliban should be removed from the blacklist, but not everyone, not those at the very top," Abdul Qader Kuchi, a delegate from Nangahar province in eastern Afghanistan, said.
Low-level Taliban members held by the US as enemy combatants at Bagram prison in Afghanistan and Guantanamo Bay, Cuba should be released, Kuchi said.
For its part, the US offered cautious support for the jirga.
"There is no military solution to most conflicts. This is not unique in that regard," Hillary Clinton, the US secretary of state, said on Thursday.
"But of course, we want to be kept fully informed."
The US has around 100,000 troops in Afghanistan.
The jirga is scheduled to end on Friday.
Several rockets were launched at the tent housing the jirga, during Karzai's opening speech on Wednesday.
Long bursts of gunfire were also heard nearby. Karzai left the area in an armoured convoy after his speech.
Separately, a suicide bomber blew himself up near the tent, according. No casualties were reported, except for the bomber.
Zemeri Bashary, a spokesman for the Afghan interior ministry, said police killed two other fighters, and captured a third, in a house near the conference site.
The Taliban claimed responsibility for the attacks.
The Taliban had warned delegates to stay away in an audio recording released last month, saying that "the punishment for participating in the jirga is death".