Ghana's President John Kufuor has held separate talks with both sides involved in Kenya's election crisis.
President Kufuor, left, held talks with both sides
Mr Kufuor - who also heads the African Union - met President Mwai Kibaki and opposition leader Raila Odinga.
Afterwards, Mr Kibaki's spokesman said he wanted to reach out to his opponents now the violence had subsided, while Mr Odinga called the talks "fruitful".
But there is no sign the two sides will meet for direct talks to resolve the violence, which has claimed 600 lives.
On Wednesday Mr Odinga refused such talks proposed by Mr Kibaki, calling the offer "public relations gimmickry" that sought to divert attention from international efforts to broker a solution.
Mr Odinga has also repeatedly said he will not join a government of national unity.
In addition to those killed, some 250,000 are feared displaced by the violence following the 27 December election in Kenya - previously seen as a beacon of stability in east Africa.
After meeting Mr Kufuor, Mr Kibaki's office issued a statement, saying he had assured Mr Kufuor he was initiating dialogue.
"Now that peace was returning to these parts, his partially formed government would continue to reach out to Kenyan leaders who would also be encouraged to play their role in preaching peace among their followers," the statement said.
Later, the Ghanaian president met Mr Odinga for four hours.
"We have given them our side of the story. This is basically in the interest of finding a peaceful resolution to the crisis that we have in our country today," Mr Odinga said.
The BBC's Josphat Makori in Nairobi reports that the mediation efforts have been generally welcomed by the public - who feel Mr Kufuor's visit will bring the calm needed for talks - but that there is widespread conviction that a home-grown solution is needed.
Kalonzo Musyoka: Vice-president, ODM-Kenya
Uhuru Kenyatta: Local government, Kanu
Moses Wetangula: Foreign affairs, PNU
Kiraitu Murungi, Energy, PNU
Martha Karua, Justice, PNU
George Saitoti: Internal Security, PNU
John Michuki: Road transport, PNU
Mr Odinga's Orange Democratic Movement (ODM) has said that it does not recognise the new cabinet announced on Tuesday by Mr Kibaki.
Earlier on Wednesday, Mr Kibaki insisted that there was room for members of the opposition in his new cabinet - currently dominated by members of his Party of National Unity (PNU), but until now only partially filled.
"When my government is fully constituted as a result of dialogue, it will be broad-based and represent the will of the people of Kenya," he said in a statement.
Following his meeting with Mr Kufuor, Mr Kibaki flew off to the western city of Eldoret, which has suffered some of the worst violence since the crisis began.
He addressed three rallies, mainly attended by members of his Kikuyu tribe who were worst affected by violence in the area.
Visibly angered by the masses of displaced, Mr Kibaki urged followers not to flee the area, promising that "those who have been inciting people and brought this mayhem will be brought to justice".
The latest violence - in which up to three people are reported to have died - was sparked by the unveiling of Mr Kibaki's cabinet and centred on districts of the capital and the western opposition stronghold of Kisumu.
The news agency Associated Press reported continuing protests on the road between the two cities on Wednesday, with dozens of youths burning tyres to block the route.
"If elections fail, violence prevails!" it quoted them as shouting.