House Republicans on Wednesday advanced spending legislation that would provide billions more dollars than what President Trump requested for foreign aid, global health, peacekeeping activities and international broadcasting in the coming year, defying Mr. Trump’s wishes for more drastic funding cuts.

The measure, if enacted, would still slash the foreign aid and the State Department budget compared with the current year, cutting it by 22 percent, to $46.2 billion. But House Republicans moved to salvage key programs that Mr. Trump is seeking to eliminate altogether, such as for peacekeeping activities, supporting democracies abroad and global health initiatives for family planning and reproductive care.

It would also provide more than four times the funding that the president has requested for international broadcasting activities, despite Mr. Trump’s push to shut down the Voice of America and other federally funded news organizations that provide independent coverage in countries with limited press freedom.

Yet even as they voted to provide money for programs the president wants to gut, Republicans proposed handing the White House more power to ignore Congress’ spending dictates altogether. They removed standard language from the spending measure that makes it more difficult for the executive branch to cancel spending that Congress has approved. That drew angry protests from Democrats, who accused the G.O.P. of abdicating the power of the purse.

“You do want to give up the authority of the committee,” said Representative Steny Hoyer, Democrat of Maryland. He accused Republicans of turning Congress into a body that “passes suggestions,” not laws.

“Stand up for America,” said Mr. Hoyer, berating his Republican colleagues. “Stand up for the committee. Stand up for the Congress. Stand up for the Constitution.”