"I was also given again an invitation to go back to China whether as a friend, official, not official visits", Duterte said.
Speaking about human rights during his Vietnam visit, Mr Duterte proposed a "world summit" on the issue - but not looking exclusively at human rights abuses in the Philippines.
Trump and Duterte are expected to hold a one-on-one meeting in Manila on Monday on the sidelines of a 20-nation summit of Asia-Pacific leaders.
In his arrival speech, Duterte said he considered his bilateral meetings with Chinese President Xi Jinping and Russian President Vladimir Putin as the "most productive" part of his trip in Da Nang. "I will slap her in front of you. Why? The US President's willingness to challenge the appalling record of President Duterte's "war on drugs" is a crucial test of his administration's commitment to upholding and defending human rights".
The comments came as the leader defended his government's brutal countrywide crackdown on drugs. "He is not the [head of the] Human Rights Commission", he said.
Mr Duterte has encouraged extrajudicial killings of those involved in the drugs trade, and said he would "be happy to slaughter" three million drug addicts in the country.
But Trump, who has been criticized at home for neglecting rights issues in dealings overseas, in May praised Duterte for doing an "unbelievable job on the drug problem".
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"Completely inappropriate photo for the head of one our most important intelligent (sic) services to be in", federal opposition member of parliament Anthony Byrne said in a Twitter post.
Duterte seemed confident he had Trump's backing for his deadly war on drugs. Bishop had previously criticised the drug war.
Duterte might also expect support from Japanese Prime Minister Shinzo Abe, who struck the pose when the pair met in Tokyo past year.
The report comes after Duterte on Sunday welcomed Trump to the Philippines on his first official visit to the country.
Duterte's aides have repeatedly told journalists not to believe everything the president says, cautioning that he often jokes or indulges in "hyperbole".
Karapatan secretary-general Cristina Palabay said it was hypocritical for the two to even discuss the topic given their tracklist of human rights violations.
"On the grounds of what both Duterte and Trump (have) done and (are) continuously doing, it is not that they do not understand the concept of human and people's rights, it is that they just do not care", Palabay said in a statement. There was also a demonstration by the LGBT community at the University of the Philippines.