The opposition in Kenya has called for a re-run of the presidential election last week, which it says was rigged.
Archbishop Tutu (R) said Mr Kibaki (L) was prepared to be flexible
An opposition spokesman said President Mwai Kibaki should step aside, and a transitional administration should hold elections within three months.
A government spokesman indicated that Mr Kibaki might accept fresh elections, under certain conditions.
More than 300 people died in violence following the election. The UN says another 180,000 have been displaced.
The head of the UN office for humanitarian affairs in Nairobi says that around half-a-million people are in acute need of assistance.
While the recent trigger for the troubles was the election, Kenyan politics has been dogged by ethnic tensions since independence in 1963.
Mr Kibaki depends heavily on support from the largest ethnic group, the Kikuyus, while the western Luo and Kalenjin groups - who are seeking greater autonomy - back losing presidential candidate Raila Odinga.
The call for an election came from Anyang Nyongo, the secretary-general of Mr Odinga's ODM party.
Military police are guarding key points in Nairobi
He also said the current electoral commission should not be involved in new polls.
"The current crisis is not caused by the Kenyan people - it is caused by Kibaki and his henchmen, who messed up the result after the Kenyan people had voted," he told the BBC.
A Kenyan government spokesman, Alfred Mutua, said the president was not in principle opposed to holding fresh elections.
"We would accept even another election, as long as the constitution is followed," Alfred Mutua told Reuters.
"If the courts decide it, we would accept that."
The opposition had earlier dismissed the prospect of taking its complaints to the courts.
William Ruto had said it would be like taking sheep to a court presided over by a hyena.
But the BBC's Grant Ferrett, reporting from Nairobi, says both government and opposition are now trying to show more flexibility.
A similar sign of flexibility was reported by South African Archbishop Desmond Tutu, after a meeting with Mr Kibaki.
"The president was not averse to the idea of coalitions - but clearly there has to be an acceptance that there is a governing authority," Mr Tutu was quoted as saying by Reuters.
"There is a great deal of hope since both the Orange Democratic Movement and the government have indicated they are open to negotiations."
Mr Tutu met Mr Odinga on Thursday.
In other developments:
- Top US diplomat Jendayi Frazer was due in Kenya for talks aimed at bringing the two sides together
- French Foreign Minister Bernard Kouchner said he believed the Kenyan elections had been rigged.
In Nairobi on Friday, the security forces appeared to have succeeded for a second day in blocking a planned opposition rally from happening. They sealed off Uhuru (Freedom) Park, the venue for the proposed protests.
Thousands of police were deployed around the city, though fewer than on Thursday.
The opposition neighbourhood of Kibera is also being patrolled
And with traffic back on the streets, some shops and businesses have re-opened, as the city attempts to return to something like a normal life.
At one point several hundred youths had gathered outside the ODM offices in Nairobi, saying they intended to press ahead with the planned protest.
But other opposition supporters have been telling the BBC they do not want to be beaten up by police.
On Thursday security forces blocked a banned mass rally in Nairobi, using tear gas and water cannon to disperse the crowds.
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%