Harvard, the world’s wealthiest university, sued the Trump administration on Monday, fighting back against its threats to slash billions of dollars from the school’s research funding as part of a crusade against the nation’s top colleges.

The lawsuit signaled a major escalation of the ongoing fight between higher education and President Trump, who has vowed to “reclaim” elite universities. The administration has cast its campaign as a fight against antisemitism, but has also targeted programs and teaching related to racial diversity and gender ideology.

Earlier this month, it sent Harvard a list of demands that included auditing professors for plagiarism, reporting to the federal government any international students accused of misconduct, and appointing an outside overseer to make sure that academic departments were “viewpoint diverse.”

Alan M. Garber, Harvard’s president, accused the government in a statement on Monday of trying to wield “unprecedented and improper control.” Dr. Garber said the consequences of the government’s actions would be “severe and long lasting.”

The Trump administration has claimed that Harvard and other schools have allowed antisemitic language and harassment to remain unchecked on their campuses. Monday’s lawsuit noted that the government had cited the university’s response to antisemitism as justification for its “unlawful action.”

Dr. Garber, in his statement, said that “as a Jew and as an American, I know very well that there are valid concerns about rising antisemitism.” But he said that the government was legally required to engage with the university about the ways it was fighting antisemitism. Instead, he said, the government has sought to control “whom we hire and what we teach.”