Philippine mayor Rodrigo Duterte appeared headed for victory in presidential elections on Monday as an unofficial tally showed him millions of votes ahead of the other candidates and one of his strongest rivals conceded the race.

Duterte, the 71-year-old mayor of the southern city of Davao, was leading with 13.21 million votes based on returns from about 80 per cent of precincts, according to the poll watchdog Parish Pastoral Council on Responsible Voting (PPCRV).

Administration candidate Mar Roxas was in second place at 7.76 million, followed by first-time Senator Grace Poe with 7.48 million votes.

Poe, who was the early frontrunner in the race, conceded to Duterte.

"I will sleep tonight with a clear conscience, satisfied that I and my camp and my supporters did everything," she said.

"I, Grace Poe, a candidate for the presidency this 2016, am conceding the race to Rodrigo Duterte who is clearly leading the tally and chosen by the majority of the people," she added.

Poe said she called Duterte before announcing her decision.

In the vice presidential race, the only son and namesake of late dictator Ferdinand Marcos was in the lead with 11.86 million votes, followed by administration candidate and congresswoman Leni Robredo at 11.43 million votes, according to the council's quick count.

"I'm feeling that by all indications we should be successful today," Marcos told reporters. "Do not allow your voices to be silenced. Do not allow the true choice of the people to be defeated."

Duterte, who was mobbed by thousands of supporters as he voted in Davao City, thanked the Filipinos who voted for him and called for reconciliation after an acrimonious campaign.

"I would like to reach my hands out to my opponents,: he told a press conference after casting his ballot. "Let us begin the healing now. We are responsible for the security of this nation. We are responsible for the integrity of this country."

The Commission on Election said voter turnout was estimated at a record 80 per cent of more than 54 million Filipinos registered to vote.

The predominantly Catholic country has an estimated population of 100 million.

While results indicate Duterte is the likely winner, only Congress can officially tally the votes for president and vice president and proclaim winners in those contest.

The PPCRV said it received numerous reports of vote-counting machines overheating and refusing to accept ballots. There were also reports of widespread vote buying, and security officials reported sporadic violence.

At least 12 people were killed in the hours after the polls opened at 6 am, including seven campaign volunteers just south of Manila, and four people in several attacks in the conflict-wracked southern region of Mindanao, according to police.

Unidentified men burned down a school designated as a polling centre in Lanao del Norte prove, while in a town of nearby Maguindanao, gunmen forced their way into another school and made off with 10 vote-counting machines before the polls opened.

Duterte has raised eyebrows for cursing, physical threats against criminals, threatening to dissolve parliament to avoid impeachment for any human rights violations, and making off-colour jokes about the rape of an Australian missionary who died in a 1989 prison riot.

But his anti-crime stance has struck a chord amid public dissatisfaction over slow progress in the administration to combat poverty, crime and corruption despite rapid economic growth.

Outgoing President Benigno Aquino, who has been credited for the economic boost, called earlier for a peaceful and credible election.

"In a democracy, everyone makes a decision," he said. "In the end, after the elections, may the bickering end."

Aquino had called on rivals of Duterte to work together to defeat him amid fears his administration would turn into a dictatorship, some 30 years after late dictator Ferdinand Marcos was ousted.

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