Kenyan President Mwai Kibaki has said he is willing to form a government of national unity.
Food distribution networks in Kenya have been badly hit
After a meeting with the US diplomat Jendayi Frazer, he said he wanted to "help in the healing" process in Kenya.
In response, opposition leader Raila Odinga indicated he was willing to negotiate, but reiterated his view that Mr Kibaki should step down.
Kenya has been beset by violence since polls last month which the opposition says were rigged in Mr Kibaki's favour.
In the latest clashes, several houses were set on fire in Nairobi's Mathare slum district, the Associated Press news agency reported, adding that one man had been shot dead by police.
And the BBC's Grant Ferrett in the western city of Kisumu says hundreds of ethnic Kikuyus were being forced to leave on buses after being targeted by opposition supporters who accused them of backing President Kibaki.
Meanwhile, the UN World Food Programme (WFP) said it expected that its convoy of 20 trucks with nearly 700 tonnes of food would leave the port of Mombasa on Sunday to help ease the crippling shortages of food across Kenya.
On the diplomatic front, the President of Ghana, John Kufuor, who also heads the African Union, is expected in Kenya next week to add his weight to the mediation effort.
Mr Kibaki said in a statement that he was "ready to form a government of national unity that would not only unite Kenyans but would also help in the healing and reconciliation process".
The statement also said Ms Frazer - the top US diplomat on Africa - had commended Mr Kibaki for reaching out to the opposition to stop the violence, and had called on all parties to embrace dialogue.
KENYA'S ETHNIC GROUPS
Population 34.5m, comprising more than 40 ethnic groups
Kikuyu are the largest tribe, mostly concentrated around Nairobi
Most of Eastern/ North-eastern regions sparsely populated with ethnic Somalis
Main ethnic groups are:
Other African: 15%
But Mr Odinga said he was not prepared to negotiate through the media, and he would only consider the proposal at official negotiations - to which he had not yet received a formal invitation.
"Our starting point is that Kibaki is there illegally. He should not come to the negotiating table as the president," he said.
But Mr Odinga showed little interest in a national unity government, saying it was a way to "cheat the Kenyans of their rights".
Mr Odinga's team has demanded that an international mediator help settle the dispute - his spokesman Salim Lone telling Reuters news agency that without such a presence, the opposition has little faith any agreement would be adhered to.
The US delegation is not releasing details of the discussions, but the BBC understands that it is pushing for a government of national unity.
More than 350 people have been killed in Kenya and 250,000 made homeless in violence since the 27 December elections.
The talks in Nairobi come amid warnings by UN officials that a humanitarian crisis was worsening across Kenya, with the west and the Rift Valley worst hit.
There is plenty of food in the country but trucks have been unable to deliver it because of vigilante violence on many roads, the BBC's Adam Mynott reports.
The WFP is providing supplies for 100,000 people in the northern Rift Valley.
"We need supplies up here urgently particularly of cooking oil and of corn-soya blend which is particularly important for feeding young children at risk of malnutrition," the WFP's Marcus Prior told the BBC.
Kenyan politics has been dogged by ethnic tensions since independence in 1963.
Mr Kibaki depends for support on the largest ethnic group, the Kikuyus, while the western Luo and Kalenjin groups - who seek greater autonomy - back Mr Odinga.