Mr Trump was condemned by human rights groups and some USA legislators for what they see as tantamount to an endorsement of Mr Duterte's bloody war on drugs, which has killed thousands of people since he took office 10 months ago.
Duterte's tirades have raised many eyebrows since he took office.
"President Trump enjoyed the conversation and said that he is looking forward to visiting the Philippines in November to participate in the East Asia Summit and the US-ASEAN summit", the Office of the US Press Secretary said. Now, there is three million drug addicts.
The White House readout of Saturday's Duterte call credited his government for "fighting very hard to rid its country of drugs".
In a statement issued after the phone call, the White House said Trump invited Duterte to the White House to discuss the US-Philippines alliance "which is now heading in a very positive direction".
"We are watching in real time as the American human rights bully pulpit disintegrates into ash" a remark made on the social media platform "Twitter" by Senator Christopher S. Murphy, Democrat of CT and a member of the Senate Foreign Relations Committee.
"The Trump administration has been unfortunately silent as to the importance of American values", said Maryland Sen.More news: Mattis tells Turkey's PM: US committed to your security
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The United States is not in a position to lecture other countries on their human rights record because it is not a beacon of human rights, says Don DeBar, an American journalist and political analyst.
Duterte has received widespread condemnation in the West for failure to curtail the killings and address activists' allegations of systematic, state-sponsored murders by police of drug users and dealers, which the authorities reject.
Reince Priebus, the chief of staff at the White House also reiterated in the Sunday morning television shows that the goal of the visit would be purely North Korea. Duterte had threatened to "break up" with his American allies amid USA criticism over Duterte's alleged human-rights violations, namely extrajudicial killings in his nation's war against drug trafficking.
But even if Duterte is too busy to make the trip to Washington, D.C., the Philippine president struck a more positive tone about USA relations while touring Chinese warships on Monday.
Mr Duterte said yesterday that his efforts to loosen the alliance were only a response to the drug war criticism. Rep. Ed Royce, the Republican chairman of the House Foreign Affairs Committee, said of the invitation: "This is not a move I would have made".
In a sign of lingering tensions between the two countries, Mr Duterte later said he might be too busy to make the trip.