Kenyan opposition leader Raila Odinga has rejected the results of the re-run presidential election that saw Uhuru Kenyatta gaining a second term.
Mr Odinga called it "a sham" but made no mention of any legal challenge.
Mr Kenyatta won 98% of the vote with turnout under 40% - less than half that recorded in August's vote, largely because of an opposition boycott.
The Supreme Court annulled the first vote in August citing "irregularities and illegalities".
In his first official reaction to the re-run, Mr Odinga called for a "national resistance movement" including the formation of a "people's assembly" to bring civil society groups together to "restore democracy". But he did not explain how that would work.
"This election must not stand .... It will make a complete mockery of elections and might well be the end of the ballot as a means of instituting government in Kenya. It will completely destroy public confidence in the vote," he said.
The BBC's Alastair Leithead in Nairobi says that Mr Odinga's response to the election result was short on substance.
The opposition leader repeated claims that the re-run of August's presidential poll was unconstitutional - lawyers from both sides are still arguing about this, and the Supreme Court has a petition pending.
"We will not allow two megalomaniacs [Mr Kenyatta and his deputy] destroy the dream of freedom and democracy," Mr Odinga said.
Mr Kenyatta, who is now set to serve a second term, said if the new results were challenged in the courts he would accept the outcome.
He has appealed for calm and promised Kenyans that "their neighbour will remain their neighbour" despite political uncertainty.
About 50 people are reported to have died in violence since Mr Kenyatta was declared the winner of August's election.
Security has been tightened in Kenya as voting takes place in a re-run of the presidential election, which is being boycotted by the main opposition.
Kenya's President Uhuru Kenyatta, who is seeking a second term, has urged people to vote and remain peaceful.
Opposition leader Raila Odinga, who has pulled out of the election re-run, has called on his supporters to stay away.
Mr Kenyatta was announced the winner in an 8 August vote but the poll is being held again because of "irregularities".
The polls on Thursday opened at 06:00 (03:00 GMT) with tens of thousands of police and other security personnel deployed to protect voters and polling stations.
However, the BBC's Alastair Leithead in Nairobi says turnout so far appears to be much lower than in the first vote.
One voter in Nairobi's Mathare slum, taxi driver David Njeru, 26, told the AFP news agency: "It is my duty to vote. Last time the queue was all around the block and I waited six hours to vote, this time the people are few."
On the eve of the vote, Mr Kenyatta urged people to cast their ballots: "Our forefathers fought and died for the right of the African to vote, we dare not reject this inheritance."
As the polling stations opened their doors, opposition protesters attempted to block roads in parts of Nairobi's Kibera slum, with riot police using tear gas in a bid to disperse the crowds.
The announcement by the Independent Electoral and Boundaries Commission (IEBC) of Mr Kenyatta's victory on 8 August led to inflammatory rhetoric and attacks on the body.
Last week, a senior member of the IEBC fled to the US amid death threats.
About 70 people have been killed in violence since Mr Kenyatta was declared the winner in August's election.
Western diplomats have warned of "growing insecurity" in Kenya ahead of Thursday's presidential election re-run, boycotted by the main opposition.
Inflammatory rhetoric and attacks on the election commission made it more difficult to hold a legitimate poll, the 20 envoys said.
Kenyan prosecutors said opposition leader Raila Odinga's sister would be charged with inciting violence.
Mr Odinga has vowed to disrupt Thursday's poll with a mass protest.
He says the vote cannot be held before key reforms, including the sacking of Independent Electoral and Boundaries Commission (IEBC) officials, are implemented.
About 70 people have been killed in violence since the IEBC declared President Uhuru Kenyatta the winner of elections on 8 August.
The Supreme Court of Appeal annulled his victory, saying the poll was marred by irregularities and illegalities.
And Mr Odinga says nothing has changed since.
The foreign envoys said they were concerned about the "deteriorating political environment" in East Africa's biggest economy.
"It is easier to tear down than to build up. But it is dangerous, and it must stop," US ambassador Bob Godec said in a statement on behalf of the 20 diplomats, including those of France, Germany and the UK.
Last week, a senior member of the IEBC fled to the US amid death threats.
Roselyn Akombe said the commission was under political "siege", unable to reach consensus or take any decisions.
Kenyan opposition leader Raila Odinga has pulled out of October's election re-run.
Mr Odinga said his withdrawal would give the electoral commission enough time to introduce reforms that will help deliver a more credible election.
The Supreme Court annulled the result of the original 8 August poll, which saw Uhuru Kenyatta declared winner, after finding irregularities.
But Mr Kenyatta says he is ready to proceed with the new vote as planned.
The country's electoral commission said Mr Kenyatta had won the August vote by a margin of 1.4 million votes - or 54% of the total, compared to Mr Odinga's 44%.
Kenya's vice-president, William Ruto, has now called on the commission to declare Mr Kenyatta president as a result of Mr Odinga's announcement.
The election re-run was due to take place on 26 October, but Mr Odinga said on Tuesday: "We have come to the conclusion that there is no intention on the part of the IEBC [electoral commission] to undertake any changes to its operations and personnel... All indications are that the election scheduled for 26 October will be worse than the previous one."
As a result, he said, "considering the interests of the people of Kenya, the region and the world at large" it was best that he withdrew from the race.
Mr Odinga's coalition party believes the election will have to be cancelled as a result of his withdrawal, allowing "adequate time to undertake the reforms necessary to conduct an election that is in strict conformity with the constitution, the relevant laws and the constitution".
But Mr Kenyatta, speaking at a rally in the southern town of Voi, said: "We have no problem going back to elections. We are sure we will get more votes than the last time."
He added: "We are also telling him it is the people's right to choose their leader. It is their sovereign right to choose their leader of choice."
Mr Odinga's opposition coalition - the National Super Alliance (NASA) - has previously made clear its participation in the election was contingent on reforms being made.
But Kenya's Independent Electoral and Boundaries Commission (IEBC) says it has made the necessary changes.
Prominent opposition senator James Orengo has called on people to protest on Wednesday, using the slogan "no reform, no elections".
Kenya's Supreme Court has blamed the country's electoral commission (IEBC) for its decision to annul the re-election of President Uhuru Kenyatta.
The judges said the 8 August poll was "neither transparent or verifiable".
Deputy Chief Justice Philomena Mwilu said the IEBC did not verify the presidential results before they were announced.
Mr Kenyatta got 54% of the vote against opposition leader Raila Odinga's 44%, according to the IEBC's results.
Mr Odinga went to court alleging that he had been cheated of victory and that the IEBC had not followed the law in the conduct of the election.
The Supreme Court took the unprecedented step of annulling the election on 1 September but it has only now explained why it took that decision.
It was the first time in Africa that a court had agreed with an opposition demand to cancel a presidential election over rigging allegations.
While the judgement was being read out, police fired tear gas outside the Supreme Court to disperse opposition supporters who had gathered to support Mr Odinga.
At one point a swarm of bees attacked some of them.
Ms Mwilu said that the commission had not complied with a court order to allow its electronic voting system to be scrutinised.
She said that the IEBC's refusal to comply with the order to grant access to its electronic voting system led the court to "accept claims by the opposition that the computer system had been infiltrated and compromised and the data interfered with, or that the IEBC officials interfered with the system themselves".
The electoral commission has disputed that its system was tampered with.
Opposition coalition Nasa has been pushing for the sacking of IEBC officials whom it blames for bungling the polls, saying that a new team should be in charge of the re-run scheduled for 17 October.
Doubts have however been cast on this date because OT-Morpho, the French company that provided the voting kits, has said that it needs to reconfigure the more than 40,000 kits and that the process would not be complete until at least the end of October.
The judges had ordered the re-run to be held in 60 days.
Four judges voted to annul the election while two dissented. Another judge was taken ill during the hearing of the petition and did not take part in the case.