Philippines President Rodrigo Duterte talks to US President-elect Donald Trump from Davao City on December 2, 2016 (AFP Photo/Richard Madelo)

Manila (AFP) - Philippine leader Rodrigo Duterte said Saturday that President-elect Donald Trump told him Manila was conducting its deadly drug war "the right way", in stark contrast to the criticism he has received from the current White House.

The Philippine president called Trump late Friday evening to congratulate him on his election victory with Trump wishing him "success" in his controversial anti-crime crackdown, in which some 4,800 people have been killed since June, according to Duterte.

"He was quite sensitive also to our worry about drugs. And he wishes me well... in my campaign and he said that... we are doing it as a sovereign nation, the right way," Duterte said in a video released by his office Saturday.

"He was wishing me success in my campaign against the drug problem."

Duterte, 71, launched an unprecedented war on drugs that drew a wave of global criticism with Obama urging the leader in September to conduct his campaign "the right way" following concerns over alleged extrajudicial killings.

Trump's office released a brief statement following the conversation, saying Duterte had congratulated Trump and the two agreed to work together closely.

Duterte won presidential elections in May after pledging to kill tens of thousands of drug suspects, warning that otherwise the Philippines would turn into a narco-state.

Since assuming office, he has called on police and even civilians to kill drug users.

Duterte also said he would be "happy to slaughter" three million drug addicts, and likened his campaign to Nazi leader Adolf Hitler's efforts to exterminate Jews in Europe.

In October Duterte announced a "separation" from the United States and had called for the withdrawal of American troops from his country, putting into question Manila's 70-year-old alliance with Washington.

But on Saturday, Duterte said he "could sense a good rapport" with an "animated" Trump.

Duterte's spokesman said the "understanding" between the two leaders signalled better Philippine-US ties.

"We can say at this stage that our relationship with the US is improving," Ernesto Abella said.

Video released by Duterte's office showed the Philippine leader laughing as he chatted on the phone, later saying Trump would would be "a good president for the United States of America".

Duterte said the president-elect invited him to visit New York and Washington DC and he returned the favour by asking Trump to attend a regional summit that the Philippines is set to host next year.

"If I'm around, he wants to be notified of my presence," Duterte said.