Mr. Trump is comfortable with the wiseguys-argot of that time and place, and he defaults to it whether he is describing his faithless lawyer or his fruitless efforts to discourage the F.B.I. director, James B. Comey, from investigating one of his senior advisers, Michael T. Flynn, over his connections to Russia.

“When I first heard that Trump said to Comey, ‘Let this go,’ it just rang such a bell with me,” said Nicholas Pileggi, an author who has chronicled the Mafia in books and films like “Goodfellas” and “Casino.” “Trump was surrounded by these people. Being raised in that environment, it was normalized to him.”

Mr. Pileggi traced the president’s language to the Madison Club, a Democratic Party machine in Brooklyn that helped his father, Fred Trump, win his first real estate deals in the 1930s. In those smoke-filled circles, favors were traded like cases of whiskey and loyalty mattered above all.