As the Trump administration slashes support to research institutions and threatens to freeze federal funding to universities like Harvard and Columbia, European leaders are offering financial help to U.S.-based researchers and hoping to benefit from what they are calling a “gigantic miscalculation.”

“Nobody could imagine a few years ago that one of the great democracies of the world would eliminate research programs on the pretext that the word ‘diversity’ appeared in its program,” President Emmanuel Macron of France said on Monday.

He was speaking at the Sorbonne University in Paris during an event called Choose Europe for Science that was organized by the French government and the European Union.

It was unthinkable, Mr. Macron said, alluding also to the withdrawal of researchers’ visas in the United States, that a nation whose “economy depends so heavily on free science” would “commit such an error.”

Ursula von der Leyen, president of the European Commission, announced an investment of 500 million euros, or $566 million, at the conference to “make Europe a magnet for researchers” over the next two years.

Although that amount is not much compared to the billions in cuts American universities face, it comes on top of the $105 billion international research program called Horizon Europe that supports scientific breakthroughs, like genome sequencing and mRNA vaccines, Ms. Von der Leyen said.

She did not mention the United States by name, but she described a global environment where “fundamental, free and open research is questioned.”

“What a gigantic miscalculation!” she said.

In Europe, there is a widespread feeling that Mr. Trump has abandoned America’s traditional support for liberty, free speech and democracy through his embrace of autocrats and the assault on science and academia. That has created strains but also a sense of opportunity on the continent, where attracting the best scientific minds to vigorous and independent universities is seen as part of a broader campaign to “rearm” Europe as an independent power.

Over the longer term, the European Commission, the executive arm of the European Union, plans to double grants for researchers who relocate and to enshrine freedom of scientific research into a law called the European Research Area Act.

“The first priority is to ensure that science in Europe remains open and free. That is our calling card,” Ms. von der Leyen said.

The Trump administration’s attack on science and threats to universities were the main impetus for the conference, which was attended by government ministers and prominent researchers from across Europe. Increasingly, the United States is seen as a strategic adversary, and opening doors to American researchers and scientists is viewed as a long-term response to that challenge.

Mr. Macron’s message to scientists was this: “If you love freedom, come help us to remain free.”

France announced its own program to lure U.S.-based researchers last month. The government promised universities and research institutions in the country up to 50 percent of the funding needed to lure international researchers, including those working in areas under pressure from the Trump administration like climate studies and low carbon energy. But no particular funding was announced until Monday, when Mr. Macron said his government would commit $113 million to the program.

Alarms in Europe began sounding when the Trump administration slashed jobs and froze science grants at leading American institutions as part of cost-cutting measures. European dismay increased when the U.S. government attacked diversity programs and attempted to dictate to universities “whom they can admit and hire, and which areas of study and inquiry they can pursue,” in the words of Harvard’s president, Alan M. Garber.

Harvard has filed a lawsuit against the Trump administration over its $2.2 billion federal funding freeze. Mr. Trump mused last week about ending Harvard’s tax-exempt status.

The U.S. government has also fired staff at U.S. centers deemed to be at the pinnacle of scientific research, including at the National Oceanic and Atmospheric Administration, the National Science Foundation, the Centers for Disease Control and Prevention and the National Institutes of Health, the world’s largest funder of biomedical research.

At the same time, some federal agencies have removed words from websites and grant applications that were deemed unacceptable to the Trump administration. Among the terms considered taboo are “climate science,” “diversity” and “gender.”

Taken together, the actions have sent a chill through academia and research institutes, with scientists worried not just for their jobs but the long-term viability of their research.

“In the United States, once a paradise for researchers, academic freedom is being challenged. The line between truth and falsehood, between fact and belief, is being weakened,” Elisabeth Borne, France’s education minister, said Monday as she opened the conference.

Universities in France have been at the forefront of attempts to benefit from a potential American brain drain. Aix Marseille University is interviewing some 300 candidates for its Safe Place for Science program, which it launched in March in response to the Trump administration’s cuts. Since then, many other universities and institutions have followed suit.

“Our self-interest, as well as our values, now command us to be the refuge for knowledge wherever it is under pressure,” said Luis Vassy, the president of Sciences Po University in Paris.

François Hollande, a former French president, has proposed a law to create a “scientific refugee” status for researchers threatened for their work in their countries.

However, some university heads and professors have criticized the initiative. They argue that while France is attempting to draw American researchers, it has also been cutting higher education and research budgets to address the country’s ballooning budget deficit.