Kenya's President Mwai Kibaki has invited opposition leader Raila Odinga for face-to-face talks over disputed elections, his office has announced.
Mwai Kibaki (left) and Raila Odinga could meet for talks on Friday
A spokesman said Mr Odinga would only accept if the talks were mediated by African Union chairman John Kufuor.
Mr Odinga says he was cheated of election victory and has called on Mr Kibaki to stand down.
He earlier called off planned nationwide rallies, saying he wanted to give international mediation a chance.
Mr Kibaki's office said the proposed talks would be held on Friday.
Mr Odinga's spokesman, Salim Lone, said that Mr Odinga would be happy to participate, but only as part of a mediation process conducted by Mr Kufuor, the president of Ghana.
Violent clashes over the results of the 27 December election have left some 600 people dead, Kenyan police say.
Some 250,000 people have fled their homes in clashes between rival political supporters, ethnic groups and the police.
The Law Society of Kenya has called for Mr Kibaki to step down, saying the election was "not credible" and the announcement of a winner "unacceptable".
After a week of clashes, some shops and businesses have re-opened in the capital, Nairobi and "matatu" mini-bus taxis have returned to the streets after several days when the city was deserted.
Mr Odinga called off Tuesday's protests after meeting the top US official for Africa, Jendayi Frazer.
"We are now assured that the mediation process is about to start," he said.
Mr Odinga said Kenya was living through the gravest crisis it had faced and condemned the violence that had taken place.
Ms Frazer said there may have been vote-rigging by both sides and that ordinary Kenyans had been let down.
"They've been cheated by their political leadership and their institutions," she said.
The police had tightened security ahead of the planned rallies
"The only way to restore the Kenyan people's rights and confidence in the system is that the political leaders have to stop the violence, because innocent people are dying."
Meanwhile, Mr Kibaki has reconvened parliament for 15 January.
Mr Odinga's Orange Democratic Movement won a majority in parliament but does not have the two-thirds needed for a vote of no-confidence in the president.
Both sides have accused the other of ethnic cleansing during a week of violence after Mr Kibaki was declared the winner.
A government ministry says 486 people have been killed but a senior police officers told the AFP news agency: "We have at least 600 dead... some bodies are still in the bushes where fighting occurred."
Mr Odinga said he understood that Ghana's President John Kufuor, current chairman of the African Union, would also be going to Kenya soon for talks.
Last week, the government said there was no need for Mr Kufuor to visit.
Many in need
Mr Kibaki had offered to form a "government of national unity" but Mr Odinga has insisted that the president step down.
The BBC's Peter Greste in Nairobi says there is no sign of this and there remains a large gap between the two sides' positions.
European Union observers have criticised the way some of the votes were counted, including anomalies between the results announced locally and nationally.
The government says it has deployed its military engineering unit to assist in unblocking the main highways to enable relief supplies to be delivered to displaced people, and for public transport to resume.
The head of the humanitarian services committee, Rachael Arunga, told a news conference in Nairobi that sufficient supplies were yet to reach thousands of displaced people in urgent need.
Ms Arunga said the Rift Valley province was the worst hit area and efforts were being made to deliver food items, tents and medicine to the displaced people.