U.S. Defense Secretary Ash Carter told a news conference following a meeting Southeast Asian defense chiefs in Hawaii that he personally found Duterte's comments "deeply troubling", though the matter wasn't discussed at the meeting.
State Department spokesman Mark Toner had earlier described Duterte's remarks, made in a rambling speech in Davao City, as "a significant departure" from America's partnership with the Philippines "and we find them troubling."
Duterte told reporters that he had been "portrayed to be a cousin of Hitler" by critics.
Noting that Hitler had murdered millions of Jews, Duterte said, "There are 3 million drug addicts (in the Philippines). I'd be happy to slaughter them.
"If Germany had Hitler, the Philippines would have ...," he said, pausing and pointing to himself.
The Anti-Defamation League, an international Jewish group based in the United States, said Duterte's comments were "shocking for their tone-deafness".
"The comparison of drug users and dealers to Holocaust victims is inappropriate and deeply offensive," said Todd Gutnick, the group's director of communications. "It is baffling why any leader would want to model himself after such a monster."
Duterte has said there will be no annual war games between the Philippines and the United States until the end of his six-year term, and his hostility may make Washington's strategy of rebalancing its military focus toward Asia in the face of an increasingly assertive China more difficult to achieve.