Two senators said that Philippine President Rodrigo Duterte could be impeached after admitting that he "personally" killed criminals when he was still a mayor of Davao City.

The hugely controversial president made the claim to business leaders on Monday that as the Davao City's mayor, he used to prowl on the streets on a big motorcycle looking for "an encounter to kill," just to show local authorities that he was capable of doing it.

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"I used to do it personally, if I can do it, why can't you?" Duterte told business executives.

More than 2,000 people have been killed by police anti-drug operations since Duterte assumed power in July. Many of them were shot while resisting arrest. Another 3,000 fatalities are being investigated, with human rights activists calling them vigilante killings.

Senator Leila De Lima, an avowed critic of Duterte, said the president's admission could be grounds for impeachment proceedings to be set in motion.

"That is betrayal of public trust and that constitutes high crimes. Mass murders certainly fall into the category of high crimes," de Lima told journalists on Thursday.

Senator Richard Gordon, the head of the senate justice committee, said that President Duterte left himself vulnerable to possible impeachment proceedings when he made his controversial remarks.

"When he says that, he's opening himself up, so what's the legal way? Then go ahead and impeach him," Gordon said, adding that he was not surprised by Duterte's remarks.

On the other hand, Duterte's allies in the country's congress have dared the president's opponents to file an impeachment motion. They say that removing Duterte through a political process is a numbers game, something the opposition does not have. There are only a handful of opposition lawmakers in the 293-member lower house of Congress.

A two-thirds vote is required to successfully impeach the president.

Meanwhile, Peter Wallace, the organizer of the business function where Duterte spoke, believes that the president's remarks were his "usual bravado."

"He talked as he often talks about drugs, and killings and criminality," Wallace said, adding that they had expected that he would, but they were not there to listen to that.

"We were there to talk to him or listen to him about business," the business executive said.

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