“Dummies!” the candidate shouted at black protesters after they interrupted his speech in Brooklyn.

“You stand between us and the murderers and the rapists and the assaulters,” he told members of New York’s largest police union, at another point, after it endorsed him.

The candidate was not Donald J. Trump. It was Edward I. Koch — a Democrat, not a Republican, and at the time he was a candidate for mayor, not president. But as the tumultuous Republican race came to New York ahead of its presidential primaries on Tuesday, Mr. Trump’s pugnacious style and often divisive messages brought back memories of the politician who, in his day, similarly personified New York City’s sometimes assertive, sometimes obstreperous id.