President Rodrigo Duterte said yesterday that he was inviting the United Nations and European Union to investigate thousands of extrajudicial killings that have been linked to his war on crime.

"I am inviting the EU… Send your best lawyer. Even the (UN) rapporteurs, come to the Philippines. I will write them a letter to invite them for an investigation," he said.

But he also said he would challenge them to a public debate, confident he can defend his anti-drug push as necessary and the killings as lawful. "After they ask me, I will ask them… I will humiliate them," he said.

Mr Duterte, a former city prosecutor, said: "The first question I will ask the rapporteur: I killed thousands? What was the name of the first victim? What happened? Where? For what reason? How was it done? What time was it?"

Police and vigilantes have killed more than 3,000 people since Mr Duterte took office on June 30.

The UN and EU have expressed concerns over the killings. In a statement, the European Parliament called on Mr Duterte to "put an end to the current wave of extrajudicial executions and killings".

Mr Duterte has responded by calling UN chief Ban Ki Moon a "fool", and giving the EU the dirty finger.

Mr Duterte remains popular despite the rising body count, on perceptions that his brutal methods have led to a dip in crime. He said yesterday his campaign had driven 60 per cent of criminals off the streets.

Senator Leila de Lima, an outspoken critic of Mr Duterte, asked the Foreign Ministry on Wednesday to have the UN look into the killings.

Ms de Lima had been leading a Senate inquiry into the extrajudicial killings.

But her colleagues unseated her as chair of the Justice Committee on Tuesday, a day after she presented as a witness a self-confessed hitman who said Mr Duterte or police officers under him ordered over 1,000 murders as part of his anti-crime campaign when he was mayor of Davao city for over two decades.

The witness, Mr Edgar Matobato, 57, was again at the Senate yesterday, where Mr Duterte's allies had him admit to lapses in his testimonies, including whether he actually heard Mr Duterte order the bombing of a mosque in Davao.

But Mr Matobato insisted he was not making up the murders. He stood by his account that Mr Duterte himself "finished off" with an Uzi submachine gun a government agent his men had clashed with in 1993.

Ms de Lima investigated the Davao killings when she was human rights commission chief in 2009.

Mr Duterte has been attacking Ms de Lima ever since.

Last month, he denounced her as an "immoral woman" for allegedly having an affair with her driver. He kept at it yesterday, saying she "is not only screwing her driver, but also the entire nation".