The White House has backed away from a plan to issue an executive order that would subject billions of dollars in federal health and biomedical research spending to heightened political scrutiny, according to four people familiar with the situation. The proposed directive would have established a commission with the power to block government research grants if the money supported work in areas that did not align with President Trump’s political agenda.

The plan was discussed in a White House meeting on Friday, and some on Capitol Hill had expected Mr. Trump to issue the order as soon as this week. But fierce opposition from both Democrats and Republicans in Congress forced the White House to recalibrate this week, according to some of the people familiar with the discussions, who described private conversations on the condition of anonymity. Nevertheless, they said, officials do not appear to have totally abandoned their desire to tighten their grip over federal research spending.

At the heart of the matter is the N.I.H., the nation’s largest research agency, which disburses much of its $48 billion annual budget to researchers who study cancer, infectious diseases and other health priorities. Historically, the N.I.H. has awarded these grants based on scientific merit after a rigorous review by experts in the relevant fields. But under Mr. Trump, political appointees have exerted extraordinary control over the grant-making process in a bid to eliminate spending seen as “woke,” and to exert pressure on Harvard University and other elite universities that the president accuses of antisemitism and liberal indoctrination.

The administration froze or cut more than 5,700 N.I.H. grants worth a total of $15 billion since Mr. Trump returned to the White House, although roughly 4,500 have been restored, some as a result of lawsuits, according to Grant Witness, a website run by research scientists. Researchers say the disruptions have created havoc in their labs. Dr. Jay Bhattacharya, the N.I.H. director, has issued new guidelines for grant-making in an effort to carry out the president’s wishes, including his opposition to diversity, equity and inclusion programs. But Mr. Trump and his budget director, Russell T. Vought, did not think the N.I.H. had gone far enough. Tensions between them erupted during a highly fractious meeting on Friday, where Mr. Vought accused Mr. Bhattacharya of funding projects in conflict with the president’s past directives, including one issued on his first day in office prohibiting federal funding for D.E.I.-related programs. News of the fiery session created a bipartisan uproar on Capitol Hill. Senator Susan Collins, Republican of Maine, who oversees the chamber’s appropriations committee, sent a letter to Mr. Vought and Dr. Bhattacharya warning that a new commission would “undermine” congressional intent and the pursuit of good science.