President Mwai Kibaki made the statement to Jendayi Frazer, the leading U.S. diplomat for Africa, according to the director of the presidential news service, Isaiya Kabira.
Kabira said he could not say whether that was a formal offer to Raila Odinga, the opposition leader who accuses Kibaki of stealing the Dec. 27 vote described by international observers as deeply flawed.
Britain, the former colonial power in Kenya, appealed Friday to leaders in the East African country to consider sharing power.
Frazer, who met with Odinga earlier Saturday, would be meeting with the opposition leader again, Kabira said, implying she might be carrying a message from Kibaki.
Odinga told a news conference he had not received any formal offer from the government, but added, "Let them put that on the table when we are negotiating."
He declined to say what his response would be, but his spokesman, Salim Lone, told The Associated Press that Odinga would rather not share power.
"Raila has said a number of times that he is not happy with (the idea of) a government of national unity, he has said he would rather remain in the opposition," Lone said.
In talks with Frazer, Odinga repeated his demand for a new election, he said.
On Friday, Odinga called for a transitional government to organize a new presidential election, but Kibaki said it could be ordered only by the High Court.
In parliamentary balloting, Odinga's party won 95 of 122 legislative seats and half of Kibaki's Cabinet lost their seats, meaning it would be almost impossible for Kibaki to govern without opposition cooperation.
There was no immediate statement from Frazer on her 90-minute meeting with Kibaki or her talks with Odinga.
Kabira read a government statement that quoted Frazer as saying that "by extending an olive branch to the opposition, President Kibaki had shown his commitment to ending the political impasse."
"She expressed optimism that all concerned parties will work together toward restoring normalcy in Kenya."
The statement said Kibaki reiterated his readiness to work with all involved parties.
"The president said 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 said.
U.S. State Department spokesman Sean McCormack said Frazer's mission is designed to complement other international efforts, including one by South African Nobel peace laureate Desmond Tutu, to encourage a peaceful solution.