Diplomatic pressure on Kenya's leaders is mounting as concerns rise over violence that has left at least 120 people dead after disputed polls.
UK Prime Minister Gordon Brown has urged both sides to work for a solution after what his government called "horrific killings".
The US government said it had "serious concerns" about the vote count.
Mwai Kibaki was officially re-elected president while Raila Odinga says he was robbed of victory by voting fraud.
There were running battles in Nairobi slums on Monday, and violence broke out at protests in Mr Odinga's home town of Kisumu.
Some of the clashes took on an ethnic dimension with the Luo community seen as pro-Odinga and the Kikuyus viewed as Kibaki supporters.
If the two sides cannot be persuaded to start talking in the next few days, there is fear that the violence could spiral out of control and turn into full-scale tribal revenge killings, says BBC diplomatic correspondent Bridget Kendall.
Kenya's Red Cross said many of the dead were killed in ethnic clashes and that gangs were checking the tribal affiliations of Red Cross workers trying to help the injured, the Associated Press reported.
Mr Brown telephoned Mr Kibaki and Mr Odinga amid diplomatic efforts to broker a compromise, urging both to work for "unity and reconciliation".
"We're appalled by and condemn the incidents of violence taking place in Kenya, including horrific killings in several Kenyan cities and towns," said UK Foreign Secretary David Miliband.
The US and the EU both expressed concern over the election.
"What's clear is that there are some real problems here and that those need to be resolved in accordance with their constitution and in accordance with their legal system," said Tom Casey, a US State Department spokesman.
"I am not offering congratulations to anybody because we have serious concerns about the vote count," he added.
UN Secretary General Ban Ki-moon urged security forces "to show utmost restraint" and appealed to Kenyans "for calm, patience and respect for law."
Mr Odinga has called for a million-strong rally by supporters in Nairobi on Thursday.
Demonstrators have been involved in running battles with police
Police banned his supporters from holding a mass alternative inauguration ceremony in the centre of the capital on Monday, a day after Mr Kibaki was sworn into office again.
In his New Year's message, the president urged reconciliation but warned that his government would "deal decisively with those who breach the peace".
Mr Odinga called on his supporters not to "ethnicise" the disputed poll. He compared Mr Kibaki to a military dictator who "seized power through the barrel of the gun."
International news agencies have counted at least 100 deaths across Kenya since Thursday's elections- with some death tolls as high as 135 - either in clashes between protesters and security forces, or in ethnic violence.
- A hospital in the north-western city of Eldoret told AFP news agency it had recorded 24 violent deaths since Saturday, with most victims either injured by gunfire or machetes
- An AFP count puts the death toll in Kisumu at 53 and that in Nairobi's slums at 48
- Seven people were killed in Nakuru, in the Rift Valley, and at least four people were killed in Mombasa
- In the coastal town of Mombasa, angry crowds on the streets set fire to cars and buildings.
Correspondents say violence was worst in the opposition stronghold of Kisumu, where a BBC reporter saw about 40 bodies with gunshot wounds at a mortuary. A witness said police had opened fire.
Police fired indiscriminately, even after the protesters started running away in the Kisumu suburbs of Manyatta and Nyamasira, an eye-witness told the BBC's Noel Mwakugu.
European Union monitors have said they were barred from counting centres.
They reported seeing altered voting forms and said results declared in Nairobi for one constituency differed from those announced locally.
Mr Kibaki's national margin of victory was 230,000 votes.
Elections chief Samuel Kivuitu has admitted some problems, including a reported voter turnout of 115% in one constituency, the Associated Press reports.