Harvard University struck a respectful but firm tone in a letter to the Trump administration on Monday, arguing that the university and the administration shared the same goals, though they differed in their approaches. It was latest move in an extraordinary back-and-forth between the school and the federal government in recent weeks.

The letter from Alan M. Garber, Harvard’s president, was sent a week after the Trump administration said it would stop giving Harvard any research grants.

Last month, the university took the government to court over what it has called unlawful intrusion into its operations. But on Monday, Dr. Garber’s tone was softer, saying he agreed with some of the Trump administration’s concerns about higher education, but that Harvard’s efforts to combat bigotry and foster an environment for free expression had been hurt by the government’s actions.

Dr. Garber said he embraced the goals of curbing antisemitism on campus; fostering more intellectual diversity, including welcoming conservative voices; and curtailing the use of race in admissions decisions.

Those goals “are undermined and threatened by the federal government’s overreach into the constitutional freedoms of private universities and its continuing disregard of Harvard’s compliance with the law,” Dr. Garber said in the letter to Linda McMahon, the secretary of education.

The university’s response came one week after Ms. McMahon wrote to Harvard to advise the university against applying for future grants, “since none will be provided.” That letter provoked new worries inside Harvard about the long-term consequences of its clash with the Trump administration.