But the Trump administration has pulled back on America’s human rights role this year, as seen in its decision announced June 19 to quit the United Nations Human Rights Council over what American officials called that group’s anti-Israel bias and double standards. Frictions over the withdrawal were aggravated by bitter exchanges between Nikki R. Haley, the American ambassador, and human rights advocacy organizations, which called the administration’s decision a mistake.

The Chinese and Russian demands for human rights cuts in peacekeeping operations have further complicated what already is an annual ordeal by the United Nations budget committee, which in principle must reach a deal before the new fiscal year begins on Sunday.

Under the committee’s procedures, a deal is done by consensus — all members must agree, which often means a flurry of last-minute give-and-take.

Some diplomats said the negotiations were likely to go into Friday or possibly Saturday.

In her 18-month tenure, Ms. Haley has made budget cutting a priority. Last year she took credit for reductions of more than $500 million to achieve this year’s peacekeeping budget of $7.3 billion. Under a complicated formula, the United States contributes about 28 percent of the money.

Secretary General António Guterres — who also wants to see peacekeeping operations run more efficiently and for less money — has proposed a budget of $7.27 billion for the coming year. Diplomats said the Americans wanted to see a reduction of about $75 million from Mr. Guterres’s proposal.

It is far from clear that the Chinese and Russian demands for job cuts, which were first reported on Tuesday by Foreign Policy magazine, will yield anywhere near the 200-plus tally that some diplomats have calculated. Nor is it clear how much money such cuts might save.

But a confidential list of budget cuts proposed by committee members, seen by The New York Times, offers a glimpse of what China and Russia have in mind.