More than 18,000 positions are at stake, including half of the seats in the upper house Senate, which has served as a bulwark against some of Duterte's most controversial policies.
Duterte is known internationally for his foul-mouthed tirades and deadly drug war, but remains hugely popular among Filipinos fed up with the country's general dysfunction and leaders who have failed to fix it.
He wants to bring back capital punishment for drug-related crimes as part of his narcotics crackdown in which thousands of alleged pushers and users have already been killed by police.
His tough-on-crime platform -- which also includes lowering the age of criminal responsibility from 15 to 12 -- was key to his landslide election victory in 2016.
Voters crowded voting centres in the capital Manila even ahead of polls opening at 6:00 am (2200 GMT Sunday) in an election where some 61 million are registered to cast ballots.
"I voted for many of the candidates endorsed by President Duterte because his government is doing its job," said Myrna Cruz, 51.
"I support their programmes, including the anti-drug campaign... but I wish the bloodshed would stop," she adding, echoing many Filipinos' nuanced backing of the crackdown.
The opening of the polls were accompanied by isolated outbursts of violence, which is not unusual in the Philippines' frequently bloody competition for elected posts.
At least 20 people have been killed and 24 wounded in election-related violence in the run up to the vote, according to an official count.
Early on Monday nine people were shot and wounded during a confrontation at a polling station on the restive southern island of Jolo, which is home to insurgents and powerful local clans, according to the military.
The violence is more frequent with the lower level races and will not likely be a major feature in the election's main contest for the Senate.
Winning a Senate majority, something that independent national surveys indicate is well within reach, would give Duterte legislative backing for his anti-crime proposals and his plan to rewrite the constitution.
Historically, the nation's 24 senators -- who serve six-year terms -- have had a reputation for being more independent-minded than the lower house.
The opposition warns that could lead to the single-term limit for the presidency being lifted, allowing him to seek re-election despite his repeated statements that he would stand down at the end of his mandate.
It would also allow him to expand his contentious anti-drug crackdown by bringing back the death penalty, a pledge that the UN Human Rights Council said gave it "deep alarm".
The Philippines outlawed capital punishment in 1987, reinstated it six years later and then abolished it again in 2006.
- Duterte's daughter -
Duterte, 74, hit the campaign trail to get his supporters in the Senate, giving two-hour speeches at late-night rallies and routinely insulting their opponents -- referring to one by an anti-gay slur and accusing another of working for communist guerrillas.
The results for municipal and city mayors and councils are expected within hours of polls closing at 6:00 pm Monday, with winners for the Senate and congressional seats likely to be declared from Friday.
Even if the presidential term limit is not lifted, the Duterte family looks well-placed to continue its reign.
The president's daughter Sara -- being eyed by some as the president's potential successor in the 2022 vote -- is running to keep her post as mayor in its southern bailiwick of Davao city.
Her younger brother Sebastian is seeking, unopposed, the city's vice-mayoral seat, while Duterte's eldest son Paolo is standing for a seat in the lower House of Representatives.