Kenyan opposition leader Raila Odinga is ahead of President Mwai Kibaki in a hard fought election, according to partial and unofficial results.
But correspondents say most of the votes still to be counted are in the president's heartland.
In a setback for Mr Kibaki, 16 of his ministers lost their seats.
Despite earlier tensions, triggered by counting delays, international observers have said the election was mainly well organised.
By 0600 (0300 GMT), the Electoral Commission of Kenya (ECK) had released results from half of Kenya's 210 constituencies, putting Mr Odinga at 2,755,111 votes and Mr Kibaki at 2,172,440 in the presidential contest, Reuters news agency reported.
But the BBC's Adam Mynott in Nairobi says Mr Odinga's lead has narrowed considerably in the past few hours and there is still a mathematical possibility that President Kibaki could snatch victory.
The ECK head, Samuel Kivuito, has said there were delays in voting and counting, and the process of compiling results was going slowly.
Isolated incidents of violence continued after the vote
Mr Odinga's Orange Democratic Movement (ODM) has in turn accused the electoral commission of deliberately delaying the results, and now says Mr Kibaki should concede.
"Kibaki seems to be going out in a very untidy manner and really is not being respectful or grateful to the democratic process that put him in power," said ODM official Anyang Ngong.
Hundreds of Mr Odinga's supporters took to the streets in the west Kenyan city of Kisumu to protest against the delays.
Some demonstrators blocked roads and looted shops belonging to members of Mr Kibaki's Kikuyu ethnic group.
Not giving up
Campaigners for Mr Kibaki continued to predict victory for the incumbent president.
"It is true that the ODM is ahead, but it's only fair to wait until the last ballot is counted before we know the winner of the elections," said Ngari Gituku, a spokesman for Mr Kibaki's Party of National Unity (PNU).
"We are not going to lose hope until the last soldier is shot down and we have no intention of giving up until such a time," he told AFP news agency, adding that his party had evidence of widespread rigging.
Police Commissioner Hussein Ali has urged poll losers to respect the outcome.
A spokesman for the ECK told the BBC that turnout had perhaps been more than 70%, from an electorate of 14m.
Early results show that a majority of MPs have lost their seats.
Kenyan parliamentarians had gained notoriety in the past five years for arbitrarily increasing their salaries and allowances while a majority of Kenyans continue to grapple with meagre wages and a high cost of living, says the BBC's Josphat Makori in Nairobi.
Vice-President Moody Awori was one of the 16 ministers who lost their seats.
He was beaten by arch-rival Dr Paul Otuoma of the ODM.
Also significant is the fall of three sons of retired president Daniel Arap Moi in three different constituencies in the Rift Valley province.
Mr Moi has helped fund Mr Kibaki's campaign.
Mr Odinga, who fell out with Mr Kibaki shortly after helping him to win the presidency in 2002, alleged fraud before the polls opened.
Mr Odinga was at first not allowed to vote on the grounds that his name was not on the voters' roll, though he did cast his ballot later in the day.
The president has denied involvement in any election fraud.
Correspondents say that in Kenya's previous elections, the outcome has been obvious before polling, or at least there has been a strong favourite.
President Kibaki hopes his economic record will secure a second term.
Mr Kibaki's critics accuse him of failing to keep his promise to tackle corruption.
There were six other candidates in the presidential elections besides Mr Kibaki and Mr Odinga.