Kenya's main TV broadcasters offerered differing, unnofficial, polls.
Based on counts of 500,000 votes or fewer, NTV and Citizen TV had Odinga leading Kibaki, while KTN put the president ahead.
Fourteen million Kenyans were eligible to vote and analysts believe between eight and 10 million did so, but the ECK gave no official turnout figures.
The elections were marred by sporadic trouble and vote-rigging charges from both sides, but the ECK dismissed the complaints.
"The electoral commission is not going to turn itself into a listening machine. Let the people of Kenya decide. Anything else is just stories," Samuel Kivuitu, the ECK chairman, told a news conference in the early hours.
On Thursday, police fired teargas to disperse an angry crowd in one voting district, while In Nairobi's vast Kibera slum, assailants shot dead one man and wounded two others near a polling station.
There has been bloodshed every election year since multiparty politics was re-introduced to Kenya in 1992, after 22 years as a one-party state.
But 2007 has so far been less violent than past elections and overall, EU and US observer teams praised the orderly fashion in which the voting took place.
"At this stage, after closing the polling stations, our observers have not obtained any evidence of fraud," said Alexander Graf Lambsdorff, chief European Union election monitor.
"But we should keep in mind that the counting and the tally are still ahead."
Several diplomats have expressed concern that a narrow victory on either side could lead to rioting by those who do not accept or trust the results.
Kibaki, who has presided over a period where Kenya's economic growth has averaged five per cent, is fighting for a second term as president before retiring to his highland tea farm after a political career spanning Kenya's post-independence history.
He has the support of his Kikuyu tribe, Kenya's largest and most economically powerful.
Odinga wants to be the first member of his Luo tribe to ascend to the presidency, the unrealised dream of his father, Kenya's first vice-president, whose falling out with Jomo Kenyatta, the country's founding president, began the Luo-Kikuyu rivalry.
Kibaki originally came to power after Odinga joined forces with him in 2002, but the two later split.
Final opinion polls released last week gave Odinga 43 to 45 per cent, ahead of Kibaki at 36.7 to 43 per cent.
Only a survey conducted by US pollster Gallup showed Kibaki on top, with 44 percent to Odinga's 43 per cent.
If Kibaki loses, he will be Kenya's first sitting president ousted at the ballot box.