Harvard University is 140 years older than the United States, has an endowment greater than the G.D.P. of nearly 100 countries and has educated eight American presidents. So if an institution was going to stand up to the Trump administration’s war on academia, Harvard would be at the top of the list.

Harvard did that forcefully on Monday in a way that injected energy into other universities across the country fearful of the president’s wrath, rejecting the Trump administration’s demands on hiring, admissions and curriculum. Some commentators went so far as to say that Harvard’s decision would empower law firms, the courts, the media and other targets of the White House to push back as well.

“This is of momentous, momentous significance,” said J. Michael Luttig, a prominent former federal appeals court judge revered by many conservatives. “This should be the turning point in the president’s rampage against American institutions.”

Michael S. Roth, who is the president of Wesleyan University and a rare critic of the White House among university administrators, welcomed Harvard’s decision. “What happens when institutions overreach is that they change course when they meet resistance,” he said. “It’s like when a bully is stopped in his tracks.”

Within hours of Harvard’s decision, federal officials said they would freeze $2.2 billion in multiyear grants to the university, along with a $60 million contract.

That is a fraction of the $9 billion in federal funding that Harvard receives, with $7 billion going to the university’s 11 affiliated hospitals in Boston and Cambridge, Mass., including Massachusetts General, Boston Children’s Hospital and the Dana-Farber Cancer Institute. The remaining $2 billion goes to research grants directly for Harvard, including for space exploration, diabetes, cancer, Alzheimer’s disease and tuberculosis.