President Trump said Tuesday that his administration was close to reaching an agreement with Harvard University, which would end a monthslong standoff that had come to symbolize the resistance to Mr. Trump’s efforts to reshape higher education.

Harvard has been seeking an end to a thicket of investigations the government has opened as part of its wide-ranging efforts to bring the university in line with Mr. Trump’s agenda.

“We are in the process of getting very close,” President Trump said on CNN. He added that the details were being finalized, and said, “They would be paying about $500 million.”

Harvard officials did not respond immediately to requests for comment.

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