Authoritarian firebrand Rodrigo Duterte warned of a "rough ride" after being sworn in as the Philippines' president on Thursday, promising a relentless war on crime and corruption but also to be a unifying leader.

Duterte, 71, won last month's election in a landslide after a campaign dominated by foul-mouthed threats to kill tens of thousands of criminals and tirades against the nation's elite that cast him as an incendiary, anti-establishment hero.

After taking his oath before a small audience inside the Malacanang presidential palace, ending the era of Benigno Aquino, Duterte signalled there would indeed be some dark days during his six years in office.

"The ride will be rough but come join me just the same," Duterte said in a short speech, with his opening remarks focused on familiar themes about the need to instil discipline in a graft-infested society.

"The problems that bedevil our country today which need to be addressed with urgency are corruption, both in the high and low echelons in government, criminality in the streets and the rampant sale of illegal drugs in all strata of Philippine society and the breakdown of law and order," Duterte said.

Duterte, a lawyer who earned a reputation as an authoritarian figure as mayor of the southern city of Davao over most of the past two decades, said these problems were symptoms of an erosion of Filipinos' faith in the nation's leaders.

- Deaths imminent -

Duterte has outlined a vision for his anti-crime programme that included reintroducing the death penalty, with hanging his preferred method of execution.

He said he would issue shoot-to-kill orders to the security services and offer them bounties for the bodies of drug dealers. He also urged ordinary Filipinos to kill suspected criminals.

During the campaign, Duterte said 100,000 people would die in his crackdown, with so many dead bodies dumped in Manila Bay that fish there would grow fat from feeding on them.

He has been accused of links to vigilante death squads in Davao, which rights groups say have killed more than 1,000 people.

Such groups are concerned that extrajudicial killings could spread across the Philippines under Duterte, with a police crackdown following his election already leaving dozens of people dead.

Duterte said on Thursday his fight against crime would be "relentless and sustained", as he called on human rights monitors and critics in congress to respect the mandate the Filipino people have given him.

But he also insisted he would work within the boundaries of the law.

"As a lawyer and former prosecutor, I know the limits of the power and authority of the president. I know what is legal and what is not. My adherence to due process and rule of law is uncompromising," he said.

- 'I serve everyone' -

Duterte also sought to portray himself as unifying figure.

"I was elected to the presidency to serve the entire country. I was not elected to serve the interest of any person or any group or any one class," Duterte said.

"I serve everyone and not only one."

During the election campaign, Duterte picked fights with the envoys of key allies the United States and Australia after they criticised his joke about wanting to rape a "beautiful" Australian missionary who was sexually assaulted and killed in a Davao prison riot.

After his election win, Duterte also launched a seemingly unprovoked attack against the United Nations.

"Fuck you UN, you can't even solve the Middle East carnage... couldn't even lift a finger in Africa (with the) butchering (of) the black people. Shut up all of you," he said.

Soon after UN Secretary-General Ban Ki-moon issued a rare rebuke of a foreign leader, criticising Duterte for saying that some journalists in the Philippines who had been murdered deserved to die because they were corrupt.

On Thursday, Duterte offered a muted message of friendship to the international community.

"On the international front and community of nations, let me reiterate that the Republic of the Philippines will honour treaties and international obligations," he said.

At a televised cabinet meeting shortly after his speech, Duterte indicated he wanted to repair relations with China that were battered during Aquino's term over competing claims to the South China Sea.

An international tribunal is due to deliver a verdict on a legal challenge filed by Aquino's administration over China's claims to most of the sea. Duterte told his cabinet members the Philippines would not "taunt or flaunt" a favourable ruling.