Philippine senators have started an investigation into the hundreds of drug-related killings under President Rodrigo Duterte's administration, as witnesses — their faces covered to protect their identities — testified Monday about how their loved ones were arrested and gunned down by police.

In her opening statement, Sen. Leila de Lima, head of the Senate justice committee leading the investigation, said she's concerned about the spate of killings that appear to have been carried out, not through legal means by the government, but by vigilantes.

"We want to know the truth behind the killings and violence. What really happened and why does this continue to happen?" de Lima said in Tagalog. "I'm not saying the killings and the use of lethal force have no legal basis, but too many have been killed for us to not be suspicious and to not question whether the rules of engagement are being followed."

De Lima said she's not suggesting that death squads are being operated by the Duterte government. Rather, she said, an investigation is needed into whether the vigilante killings are the results of an organized effort by groups from either inside or outside the government.

"As I have said, my concern does not only revolve around the growing tally of killings reported by the Philippine National Police," de Lima said. "What is particularly worrisome is that the campaign against drugs seems to be an excuse for some — may I just emphasize, some — law enforcers and other vigilantes to commit murder with impunity."

Duterte, a controversial former mayor and prosecutor who rose to power after a landslide presidential election victory in May, has publicly advocated the killing of suspected criminals, urging citizens to take matters into their own hands if they feel it's necessary.

"Shoot him and I'll give you a medal," Duterte said in June, according to the Associated Press.

Duterte's war on drugs has so far resulted in hundreds of drug-related deaths. Thousands of people also have surrendered.

Different media outlets have reported varied totals. The AP said at least 1,779 drug suspects have been killed, including more than 700 who were gunned down in confrontations with police. Reuters reported that about 1,800 drug-related killings have occurred since Duterte took office.

Last week, Philippine National Police Director General Ronald dela Rosa reported to the Senate committee that 665 drug suspects were killed in police operations from July 1 to Aug. 15. Another 899 drug-related killings within the same time period were committed by unknown assailants.

De Lima said the killings amount to about 35 a day.

Shortly before the Senate investigation began, Duterte accused de Lima of having an affair with her driver and bodyguard, who allegedly collected money from drug lords detained in the New Bilibid Prison in Muntinlupa City, Metro Manila, when de Lima was justice secretary in the previous administration.

Duterte elaborated on those accusations during a news conference Sunday night in Davao City, where he served as mayor before becoming president. The Filipino leader spoke for more than two hours, claiming that de Lima authorized her former lover to allow inmates to receive special privileges and contraband, such as guns, alcohol and drugs.

"The crux of the matter is if I do not talk about the relationship with de Lima to her driver, then there is no topic to talk about, because what is really very crucial here is the fact that because of that relationship with her driver, which I termed immoral because the driver has a family and a wife, gave rise to the corruption of what was happening inside the national penitentiary," Duterte said. "The furthest from my mind was to derogate your person. I have to mention your relationship because it was your driver who was in contact with the rest of the guys there inside prison."

De Lima has denied the allegations, challenging Duterte to shoot her if he finds real evidence of her alleged involvement with illegal drugs, according to the Philippine Star. She said her driver, who had been working for her before she entered politics, left his job last year and is now in fear that he will be captured and forced to testify against his former boss.

In her own news conference last week, de Lima said the allegations are simply a distraction from the real issues, calling them blatant efforts by Duterte to discredit her. She also said that inmates from the national penitentiary are being forced to lie about her.

Brash-talking Duterte has earned international notoriety for controversial and strongly worded statements.

Most recently, Duterte, nicknamed "The Punisher," insulted and threatened to leave the United Nations in response to criticism of his approach to combating drug problems.

"If you are that insulting, son of a bitch, we should just leave," Duterte said in Tagalog, according to CNN. "Take us out of your organization. You have done nothing anyway."

However, Foreign Secretary Perfecto Yasay Jr. said Monday that the Philippines has no plans to break away from the United Nations, the AP reported.

During Monday's hearing, about a dozen witnesses were scheduled to testify before the Senate committee. One of them, Harra Besorio, told senators that policemen illegally arrested her boyfriend and father and beat them up in front of her, the AP reported. The two were later shot and killed.

Besorio also said police searched her house without a warrant, even forcibly stripping her 2-year-old daughter naked to check if the child was being used to hide illegal drugs. No drugs were found.

Commission on Human Rights official Gilbert Boiser said the deaths were human rights violations, the AP reported.

The police officers accused of killing Besorio's husband and father have been charged with murder, according to the AP.