Both Trump and Xi were following on from the latest APEC (Asia-Pacific Economic Cooperation) summit that concluded Saturday in the coastal city of Danang, 470 miles (750 kilometers) south of Hanoi.
"What makes the death of people in the Philippines more important than the rest of the children in the world that were massacred and killed?"
"You want to ask a question, I'll give you an answer".
Meanwhile, Duterte told Xi in Vietnam that he will raise the dispute over the South China Sea as chairman of the Association of Southeast Asian Nations Summit this week.
"When I was a teenager, I was in and out of jail", said President Duterte.
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Since Mr Duterte took office in June 2016, more than 7,000 people have been killed in a brutal clampdown on illegal substances, with the leader saying he would be "happy to slaughter" three million drug addicts. "The peoples' opposition would further grow and we will hound Trump with continuous protests", Zarate said.
Speaking to the local Filipino community in the Vietnamese city of Danang on Thursday, Duterte also threatened to slap a United Nations rights rapporteur if he met her, and used obscene language to hit back at critics of his deadly drugs crackdown.
"A real person. During a rumble.
This time, with double the enthusiasm and gratitude of my country, the Philippines", Duterte said in his meeting with Putin.
"One fight there, one fight here, and at the age of 16, I killed someone".
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Philippine presidential spokesman Harry Roque told CNN before the visit that he sees Trump and Duterte as "very much alike". It was just over a look.
Amy Searight, senior adviser of the Southeast Asia Program at the Center for Strategic and International Studies, told reporters before the trip that she expects Duterte to roll out the red carpet for Trump because he "sees this as an opportunity to somewhat reset US-Philippine relations".
In an election campaign rally Duterte also said he was expelled from college for shooting a fellow student who was insulting him.
Duterte goes into the event appearing confident that even his most outrageous remarks and actions will be ignored, having boasted in the lead-up he once stabbed someone to death, while at the same time proposing to host a global human rights summit. The problem with these pests, they invite (UN) human rights commission and all, only to show the statistics: here, 10,000 died.
They are expected to hold one-on-one talks on Monday and, if Trump does not bring up any human rights concerns, Duterte is widely expected to trumpet the meeting as an endorsement.
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According to campaign group the Fawcett Society, it could take as long as 100 years to drive down the disparity in earnings. While Wales (8.3%) and Scotland (11.1%) fall below the United Kingdom average, London has the largest gap at 20.7%.