Senator Marco Rubio, a Florida Republican, and two Democratic senators — Edward J. Markey of Massachusetts and Chris Coons of Delaware — said in a letter to the department that the antidrug push “appears to be a campaign of mass atrocities thinly disguised as a response to a public health emergency.”

“Rather than address the systemic problems related to the country’s drug crisis, invest in treatment programs, or approach the epidemic with a focus on the health and well-being of the Philippine people,” the letter said, “President Duterte has instead pledged to kill another 20,000 to 30,000 people, many simply because they suffer from a drug use disorder.”

Mr. Duterte, a populist who has made international headlines for his tough talk, attacked Mr. al-Hussein without mentioning him by name during a news conference on Thursday in Manila, the capital.

“You idiot, you do not tell me what to do,” he said. “Your understanding of international law is lacking. We are the ones contributing to the United Nations. You morons! You sons of whores! And I pay your salaries. Do not open your mouth there. I employ you.”

The Philippines is among the 141 members of the 193-member United Nations that have paid their 2016 dues in full. According to the General Assembly’s Committee on Contributions, which keeps a public tally, the Philippines paid its $4.11 million assessment as of March.