Clashes between police and protesters began quickly after polls opened at 6am local time (03:00 GMT). More than 19 million voters are registered to cast their vote in the election.
Voting was officially closed at 5pm (14:00 GMT). But in some areas, voters who were lining up before the closing time, were allowed to cast their ballots. Voting in some areas have reportedly been postponed to Saturday.
Al Jazeera's Catherine Soi confirmed a man had been shot in Kisumu, the stronghold of opposition leader Raila Odinga, as police and protesters clashed. The victim was a 19-year-old male who had been shot in the thigh and bled profusely, Soi said.
Our correspondent reported that another fatality has been brought to the mortuary by rescue workers. She also reported that a third person was confirmed dead, although the circumstances leading to the person's death are still unknown.
Several others were injured, Soi said, confirming that police had fired tear gas.
The rerun comes after the Supreme Court nullified the August 8 presidential poll results because of "irregularities and illegalities" in the voting process.
At least 67 people were killed in the post-election violence following the August vote, according to Amnesty and Human Rights Watch.
President Uhuru Kenyatta, 55, is seeking a second and final five-year term in office. He won 54 percent of the votes in the nullified poll.
His main challenger, Odinga, who received almost 45 percent of the votes in August's election, is boycotting Thursday's vote.
Demonstrations in the opposition stronghold of Kibera in the capital also turned violent, with Odinga supporters burning tyres and barricading roads as police fired tear gas and live ammunition at protesters.
|Raila Odinga said opposition demands had not been met [Natalia Jidovanu/Al Jazeera]|
'No point in voting'
At least one polling station in the neighbourhood was closed.
"There is no point in voting. It is illegal what they are doing. They will steal again. This is sham. I'm not going to waste my time in voting," Alfred Otieno, a young stall owner in Kibera, told Al Jazeera.
In Kisumu, Odinga's stronghold, some polling stations were open, but there was no sign of voters.
"Do not participate in any way in the sham election. Convince your friends, neighbours and everyone else to not participate," Odinga told his supporters at a rally in Nairobi on Wednesday.
"We advice Kenyans who value democracy and justice to hold vigilance prayers or stay at home."
|None of the candidates competing against Kenyatta has a chance at winning Thursday's vote. They all scored less than one percent in August [Hamza Mohamed/Al Jazeera]|
Odinga, 72, said opposition demands to reform the electoral body following the court ruling had not been met.
After successfully challenging the results of the August poll, Odinga has called on his supporters to stay away from Thursday's vote.
Although opposition supporters heeded Odinga's call, queues had already formed at some polling stations in the Kenyan capital on Thursday before sunrise.
Amid tight security, Elastus Maina, a 40-year-old businessman, told Al Jazeera: "I queued up from 5am. It took me less than five minutes to vote. Very smooth. I'm happy with how it is going. I'm voting again because it is my democratic right. I never boycotted an election and will not do that now."
In the government stronghold of Banana, Kiambu county, people formed lines at a polling station to cast their vote, but turnout was lower than the August election.
None of the six other minor candidates competing against Kenyatta received more than one percent in the previous poll.
|Security was high after weeks of deadly protests leading up to the vote [Hamza Mohamed/Al Jazeera]|
Esther Muhindi, a 43-year-old HR manager, said she was pleased with the process on Thursday.
"I voted because the court told us to. I hope there is no more repeats. This time the queues were moving fast," she told Al Jazeera.
Thabo Mbeki, former South African president and the head of the African Union's monitoring mission to Kenya, said that observers were keeping a close watch on developments.
"We have been to two polling stations so far. In the two places we have been, there are lots of people who have turned up to vote," he said in Nairobi. "We need to have a look at more stations to see how the population is responding."
Kenyatta is the son of the country's founding father while Odinga, a former prime minister, is the son of the country's first vice president.
On Wednesday, the Supreme Court was unable to raise a quorum of judges to decide on whether the poll should go ahead.
The petition was brought by three human rights activists who claimed the electoral commission is not ready to hold a credible poll.
The East African country has witnessed almost daily street protests following the announcement of August's presidential election result.
|A voter who rose early makes her choice at a polling station in Nairobi, the capital [Hamza Mohamed/Al Jazeera]|
Source: Al Jazeera News