Manila, Philippines (CNN) Philippines President Rodrigo Duterte vows there will be no letup in his hard-line crackdown on drugs and related crime despite global concerns over the alarming death toll and possible human rights violations.

More than 1,800 people have died in police-related killings and unsolved slayings often attributed to vigilantes since Duterte took office in late June, according to police statistics.

On Tuesday, Duterte promised to fight the drug problem "tooth and nail."

"The fight against drugs will continue to the last day of my term," Duterte said at Malacañang Palace. "The fight against corruption will continue for six years maybe. ... Many will be unhappy, but I think the bigger picture is that I would have something to live by for my country."

The President spoke as the country's top police officer testified at a two-day congressional inquiry launched to explain the rise in these killings.

Philippines National Police Chief Ronald Dela Rosa told a Senate committee that more than 700 drug traffickers and users had been killed in police operations since July 1.

Dela Rosa said that 300 of his officers were suspected of involvement in the drug trade and would be relieved of their duties and tried in court.

He added that the police "follow the rule of law" and that there was no shoot-to-kill order despite the growing toll of bodies piling up in the wake of Duterte's crackdown.

Dela Rosa also said that the police's "knock and plead" campaign aims to have 1.8 million drug offenders surrender to authorities over the next six months.

In the "knock and plead" operations, police invite suspected drug users to submit themselves to local authorities for registration.

He said he was aware he had set an unachievable target for the surrender program but believed he could achieve 60% to 70% of the figure. Already, municipalities across the country have logged around 675,000 voluntary surrenders, Dela Rosa has said.

He said that the statistics would be legitimate. "We can't force people who are not using drugs to surrender, just so we can reach the target."

'We make mistakes,' police chief says

Responding to questioning by Sen. Gregorio Honasan, Dela Rosa admitted that his officers "made mistakes."

"We are only human, and we can feel frustration ...," he said.

"We admit we make mistakes, we are not perfect. We hope there is balance when they portray us."

He added, "I feel it when I go to the field, people hold my hand and say thank you for doing this. They're happy with what the police are doing."

Victims' families take the stand

On Monday, witnesses took the stand in the Senate to testify about the bloody legacy of Duterte's war on drugs. They were shrouded to protect their identities from police, who they say are responsible for the extrajudicial killings of their husbands and sons.

The Senate inquiry examined testimony from both the families of those killed -- many by police -- and also from ranking officials.

Duterte has repeatedly said the killings of drug suspects are lawful if police are acting in self-defense.

War on drugs out of control?

JUST WATCHED A brutal war on drugs in the Philippines. Replay More Videos ... MUST WATCH A brutal war on drugs in the Philippines. 03:24

The war on drugs has widespread support, with Duterte enjoying a 91% approval rating at the end of July, largely due to his hard-line position.

However, backing for his policies isn't unanimous, and Sen. Leila De Lima, one of Duterte's most outspoken critics, convened this week's hearings.

De Lima said she would put aside her war of words with Duterte to ensure the probe into the extrajudicial killings will be conducted "in the most professional manner."

She calls the crackdown a "very important issue of public interest," saying that even the international community has taken notice of "this phenomenon of summary executions."

Dela Rosa, citing data from the Dangerous Drugs Board , said Tuesday that 756 suspects have been killed in police operations since the war on drugs began, and that internal police investigations in these cases are ongoing.

PNP Chief Dela Rosa on vigilante killings: These are "deaths under investigation" https://t.co/sDo55hwVGt https://t.co/UA3HPzN2Xx — CNN Philippines (@cnnphilippines) August 22, 2016

Deaths attributed to vigilantes

Dela Rosa also faced grilling from Sen. Antonio Trillanes about the police response to 1,160 drug-related killings that have occurred since the beginning of July. Many of those have been attributed to vigilantes.

The police chief said the cases are under investigation and he's encouraging officers to fast-track them. He insisted the police were not involved in the deaths. "We have nothing to do with the vigilante killings."

The nation's top officer, who was elevated to the role when his longtime friend, confidante and colleague Duterte was elected, testified that his officers had arrested 10,153 drug pushers and users since the crackdown began.

In 6,000 police operations, 756 people have so far been killed, he said, and as a result of the raids, drugs worth $51 million (2.38 billion pesos) have been seized. CNN could not independently verify the figures the government provided.

The police does not and will not condone vigilante killings, Dela Rosa said, asserting that these have been perpetrated by crime syndicates. "The police will ensure, enforce the full force of the law against them. I hope this hearing will help bring a resolution to the drug problem," he said.

The Philippines National Police "remains loyal to our mandate."

Human Rights Watch: 'Duterte is steamrolling the rule of law'

Rights groups are condemning Duterte's violent approach to drug crime.

"Duterte is steamrolling the rule of law and its advocates both at home and abroad," said Phelim Kine, deputy director for Human Rights Watch's Asia Division.

"He has declared the soaring number of killings of alleged criminal suspects as proof of the 'success' of his anti-drug campaign and urged police to 'seize the momentum,' " Kine writes on Human Rights Watch's website.

"He has sought to intimidate domestic critics of that campaign and dismissed international critics as 'stupid.' Other countries, including the United States and European Union members, should make it clear to Duterte that inciting such violence is unacceptable and will reap potentially severe diplomatic and economic costs, beyond the human one."

Duterte has threatened to leave the United Nations in response to criticism of his approach to drug crimes.