By Manuel Mogato and Karen Lema

MANILA (Reuters) - Firebrand Philippine President Rodrigo Duterte on Thursday invited U.N. Secretary-General Ban Ki-moon and the European Union to investigate his deadly anti-drugs crackdown, after hurling insults at them for interfering in it.

Duterte has taken aim at just about anyone critical of his 11-week-old war on drugs, in which nearly 3,000 people have been killed, according to police, who have adjusted their figure from 3,800 cited last week.

He last month called the United Nations "inutile" and threatened to withdraw the Philippines from it. He gave a middle-finger gesture on Tuesday to the EU, to which he said "fuck you", twice.

"I am inviting the United Nations' Ban Ki ... what's the name of that devil? ... Ban Ki-moon," Duterte said at the opening of a new power plant.

"I am inviting the EU, send the best lawyers of your own, also the rapporteurs, to come to the Philippines. I will write them a letter to invite them for an investigation."

He later added, without elaborating: "Investigate me ... this will not be a one-way affair".

Duterte's defiance of high-profile organizations and his insults of anyone from U.S. President Barack Obama to Pope Francis has been a source of amusement for Filipinos but of concern to diplomats.

Treaty ally the United States has borne the brunt of many of his tirades, with some analysts predicting Duterte would seek to diversify foreign relations beyond Washington, including by seeking better ties with erstwhile maritime foe China.

He gave a hint of that in his speech, telling Chinese businessmen: "You will see me often in China".

He did not elaborate, but said he planned to visit China some time this year and would press his case for it to let Filipinos fish unimpeded at the disputed Scarborough Shoal.

'SCARY SCENARIO'

He also said he would debate Ban and the EU on human rights, and denied that police were involved in vigilante killings. Police say about two thirds of the deaths in the drug campaign were caused by unknown assailants and the rest in police operations.

"These were the handiworks of their co-conspirators in drugs," he said. "That's not the work of government."

Duterte resumed attacks on his biggest critic, Leila de Lima, a senator whose investigation into his drugs war appears all but over after she was unseated as head of a Senate probe.

Justice Secretary Vitaliano Aguirre on Thursday told a radio station De Lima would be charged with involvement in the drugs trade herself. A conviction could see her spend 30 years in jail.

Duterte has attacked the credibility of De Lima repeatedly, accusing her of having an affair with her staff and making money from bribes and drugs deals in one of the country's biggest prisons.

De Lima denied allegations she colluded with drugs gangs, calling them "very outlandish, very outrageous" and "laughable".

She said she no longer felt safe and was receiving hundreds of threats and hate messages.

There are also several complaints about her lodged with a house ethics committee and De Lima is facing a possible expulsion from the Senate.

Political analyst Earl Parreno said there was a danger that De Lima's ostracism after taking on Duterte would discourage others and threaten the system of checks and balances.

"It's a scary scenario," Parreno said of the possible case against her.

"It will set a precedent. It will be a clear tyranny of the majority and will eliminate all opposition to Duterte."

(Editing by Martin Petty, Robert Birsel)