"I would deal with President Trump in the most righteous way, welcome him as an important leader", Duterte said, according to Reuters.
HRW's Kine issued such call ahead of President Rodrigo Duterte's state visit in Japan on October 29-31 for talks with the Japanese Prime Minister.
He will be in Manila on the last leg of his trip, which includes visits to Japan, South Korea, China and Vietnam, to attend the ASEAN leaders' summit.
Duterte said he will discuss the regional threat posed by North Korea in his meeting with Prime Minister Shinzo Abe on Monday.
The group said 7,000 suspected drug users and drug dealers have been killed by police and "unidentified gunmen" since Duterte took office.
The Foreign Affairs department said in a statement that the President's trip was aimed at enhancing economic, political and maritime relations between the two countries.
The two leaders last met in the Philippines when Prime Minister Abe was in the country for a two-day visit.
Protesters storm Kurdistan parliament after Barzani announces resignation
The letter was read in front of the Kurdish Parliament in Irbil and posted on the official Kurdistan region presidency website. Barzani has been president of KRG since 2005 and has continued to serve in the role despite his term expiring in 2013.
The acid-tongued Duterte often curses critics, including former US President Barack Obama, and is known to shun formal protocols.
Kine added aside from "decrying Duterte's killing campaign", the Japanese Prime Minister should also demonstrate support for a United Nations-led investigation on the deaths related to the drug war.
"We are anxious. If anything can go wrong, it will go wrong", Duterte told reporters in Davao City, speaking on behalf of himself and Trump.
Duterte says "a nuclear war is totally unacceptable" and "somebody has to talk to Kim Jong Un".
The violent president of The Philippines wants to help President Donald Trump contain another murderous strongman: North Korean dictator Kim Jong Un.
Duterte has appeared eager to take down Kim, calling him a "son of a bitch" and a danger to other countries, but he has not announced any actions to repudiate the regime. He will also seek assistance in rebuilding Marawi city, heavily damaged during fighting between government forces and militants affiliated with Islamic State, and discuss ways to boost trade between the two nations, he said.