David B. Rivkin Jr., a constitutional lawyer who worked in the White House and the Justice Department under Presidents Ronald Reagan and George Bush, said critics were overreacting. While Mr. Trump’s bellicose tweets and direct involvement are unusual, he said, it would not be any different legally had he gone through his White House counsel, Donald F. McGahn II.

“What he did was not only perfectly constitutional but was not unreasonable,” Mr. Rivkin said. “He perhaps could have done it more elegantly, maybe he should have used McGahn, but he is who he is and we shouldn’t hold it against him. Just because something isn’t elegant doesn’t mean it’s wrong.”

Mr. Rivkin and others said Mr. Trump was right to see the use of an informant as an abuse of power, equating it to F.B.I. surveillance of civil rights and antiwar groups in the 1960s. Jonathan Turley, a law professor at George Washington University, said that while the way Mr. Trump went about seeking an investigation was “clearly inappropriate,” the emerging facts merited an examination.