President Trump on Thursday directed his sons to fire an outside ethics counsel for the family business because the lawyer also represents Harvard University, one of Mr. Trump’s targets in his crackdown on the nation’s top colleges.

In a social media post, Mr. Trump said the lawyer, William A. Burck, should go because of his ties to Harvard. The university sued the Trump administration after it threatened to slash billions in funding unless the school complied with a list of demands.

“Harvard is a threat to Democracy, with a lawyer, who represents me, who should therefore be forced to resign, immediately, or be fired,” Mr. Trump wrote about Mr. Burck, a comanaging partner at the firm Quinn Emanuel. “He’s not that good, anyway, and I hope that my very big and beautiful company, now run by my sons, gets rid of him ASAP!”

In a statement, one of the sons, Eric Trump, confirmed that the Trump Organization intended to cut ties to Mr. Burck over his decision to represent Harvard.

“I view it as a conflict, and I will be moving in a different direction,” he said.

Mr. Burck declined to comment.

The move underscored not just the entanglements between the Trump presidency and his private company but also the degree to which Mr. Trump will look to target people he believes have wronged him.