Kenya's ruling party and opposition could be just days away from a final political settlement to end post-election bloodshed, officials say.
Ex-UN Secretary General Kofi Annan told reporters in Nairobi an agreement could be reached next week but that earlier reports of a deal had been premature.
The BBC's Karen Allen in Nairobi says it is a significant development which could pave the way to power-sharing.
Some 1,000 people have died in clashes since the 27 December elections.
With the political crisis apparently easing, Kenya's internal security minister on Friday lifted the ban on public rallies that had been imposed after the violence broke out.
"Security has generally improved," said George Saitoti, explaining his decision, but he urged those holding rallies not to use them as "avenues to incite violence".
The decision followed Friday's second face-to-face talks between President Mwai Kibaki and opposition leader Raila Odinga - only the second time they have met since the disputed elections.
On the talks, Mr Annan said: "We are all agreed that a political settlement is needed, that a political settlement is necessary and we are working out the details of such a settlement."
President Kibaki's side said there had been an "agreement in principle", while the opposition spoke of a "positive development".
'Shift in mood'
The apparent breakthrough came as a policeman accused of shooting dead two protesters pleaded not guilty to murder at a court in Nairobi.
Footage of Constable Edward Kirui confronting protesters in the western city of Kisumu in January had been broadcast on Kenyan television.
HAVE YOUR SAY
I think in the present circumstances this is the best solution. The two sides need to put aside their personal ambitions for the sake of Kenya
Our correspondent says there has been a shift in mood in the political process, and the deadlock appears to have been broken, making way for a new sense of optimism.
Mr Odinga has previously rejected any suggestion of power sharing, while President Kibaki has insisted he is Kenya's duly elected leader.
Speaking at a prayer service in Nairobi earlier on Friday, Mr Kibaki said he was "encouraged by the commendable progress" at the peace talks.
Government negotiator Mutula Kilonzo was quoted by Reuters news agency as saying: "We cannot afford our people using bows and arrows, people being pulled out of buses to be asked 'which language do you speak?' and then being chopped."
Hundreds of thousands have been displaced in the violence
Mr Kibaki was declared the winner of the election, which observers said was deeply flawed and the opposition Orange Democratic Movement claimed was rigged.
More than 300,000 people were displaced in the ensuing violence as both sides traded accusations of ethnic cleansing.
Mr Annan arrived in Kenya last month accompanied by ex-Tanzanian President Benjamin Mkapa and Graca Machel, wife of former South African President Nelson Mandela.
UN under-secretary for humanitarian affairs John Holmes is due on Saturday to visit Kenya's Rift Valley, which has witnessed some of the worst violence in recent weeks.