On the Senate floor on Monday, Senator Mitch McConnell, Republican of Kentucky and the majority leader, said leaders in Beijing and Hong Kong must “de-escalate.” He added he was working to try to bring the Hong Kong Human Rights and Democracy Act to a floor vote.

The bill, which passed the House by unanimous consent, would mandate the executive branch to impose sanctions on Chinese and Hong Kong officials who carry out human rights abuses and review annually the favorable trade status that Washington grants Hong Kong. Mr. McConnell has been criticized for delaying a floor vote on the bill.

He said Monday that the administration already had “significant tools” it could use to support Hong Kong protesters, and urged President Trump to be more vocal on Hong Kong.

“I would encourage this president, who has seen Chinese behavior for what it is, with clarity that others have lacked, not to shy away from speaking out on Hong Kong himself,” Mr. McConnell said. “The world should hear from him directly that the United States stands with these brave men and women.”

Mr. Trump rarely talks about human rights, and he has not consistently made strong remarks on Hong Kong. In June, he told China’s leader, President Xi Jinping, that he would refrain from speaking publicly on Hong Kong as long as negotiations to settle a trade war between Washington and Beijing were progressing. His most forceful remarks on Hong Kong were in a speech in September in front of the United Nations General Assembly; he spoke of the conflict in the territory while praising the authoritarian Mr. Xi.

Mr. McConnell on Monday also spoke of the threat to Muslim ethnic minority groups in the Xinjiang region of northwest China by pointing to a New York Times report published on Saturday of 403 pages of leaked Communist Party documents on the system of internment camps there. The camps have been used to hold at least one million Muslims, and the documents show Mr. Xi set the policy starting in 2014.

Mr. McConnell said the documents were “a handbook for this Orwellian campaign to effectively erase a religious and ethnic minority in a region that is supposed to be legally distinct from the rest of China.” He added that the campaign was “chilling” and “systematic.”