His first comments on the result came after four of the seven election commissioners said they stood by their decision a day earlier to disown figures announced by electoral commission chairman Wafula Chebukati.
The dramatic series of events has raised fears of violence like that seen after past disputed polls in East Africa's richest country, including after the 2007 presidential vote when more than 1,200 people were killed in widespread clashes.
Overnight, Odinga's supporters battled police and burned tyres in the western city of Kisumu and the capital Nairobi's huge Kibera slum, but quiet had returned to the streets by Tuesday morning.
"Our view is that the figures announced by Chebukati are null and void and must be quashed by a court of law," said Odinga, a veteran opposition leader and five-time presidential candidate who was backed this time by outgoing President Uhuru Kenyatta.
"What we saw yesterday was a travesty," he told reporters, but appealed to his supporters to remain peaceful. "Let no one take the law into their own hands," he said.
Odinga broadcast the dissenting commission members' news conference at his own venue before taking the stage. He said he was not yet prepared to announce specific legal steps.
Odinga has until next Monday to file a challenge with the supreme court.
Speaking for the four commissioners, electoral commission deputy chair Juliana Cherera said the results showing Ruto winning with 50.49% were erroneously aggregated and that Chebukati had disregarded concerns about the tally raised by other commissioners.
Cherera said there were 142,000 votes that had not properly been accounted for, which might be enough to affect the outcome of the election given the narrow margin of 233,000 votes that separated Ruto and Odinga.
Reuters was unable to reach Cherera or the election commission for comment on those figures.
With memories still fresh of post-election bloodshed in 2007 and again in 2017, when more than 100 people were killed, Odinga has faced calls from home and abroad to commit to resolving any concerns in the courts.
At a crowded restaurant in Odinga's stronghold of Kisumu there was sporadic applause as supporters watched his statement rejecting the results and calling for peace. Outside the streets were quiet.
"There is no need for protest because we have evidence that Ruto rigged this thing," said Justin Omondi, a businessman and Odinga supporter.
Even so, the protests overnight showed how quickly tensions could escalate. Many shops in Kisumu were shuttered on Tuesday, and roads were dotted with large stones and marks from burned tyres.
Nancy Achieng arrived on Tuesday morning to find the wooden stall from which she sold foods at the side of the road in the Kondele neighbourhood destroyed.
"I've lost the election and I've also lost my business," said Achieng, who had been selling beans, chapati and roasted maize there for two years.
Kenya's Eurobonds slipped after the statements by Odinga and the commissioners but were still up on the day having recovered some of the sharp falls seen on Monday.
Its 2024 dollar-denominated bond was up 1.86 cents on the dollar at 88.5 cents at 1400 GMT compared to over 92 cents late last week.
Once in office, Ruto will confront an economic and social crisis as well as rising debt. Poor Kenyans already reeling from the impact of COVID-19 have been hit by global rises in food and fuel prices while a devastating drought in the north has left 4.1 million people dependent on food aid.
The 55-year-old had made Kenya's class divisions the centrepiece of his campaign to become Kenya's fifth president, promising to reward low-income "hustlers."
In his victory speech on Monday, Ruto vowed to be a president for all Kenyans. Outgoing president Kenyatta, who was not eligible to run after serving two five-year terms, fell out with his deputy Ruto and had thrown his support behind Odinga.
(Reporting by Duncan Miriri, George Obulutsa and David Lewis in Nairobi, Ayenat Mersie and Kevine Omollo in Kisumu; Additional reporting by Rachel Savage in London; Writing by James Macharia Chege and Aaron Ross; Editing by Catherine Evans)
By George Obulutsa and Ayenat Mersie