JERUSALEM — America’s top diplomat in Jerusalem lives in an elegant three-story stone house first built by a German Lutheran missionary in 1868, a short walk from the historic Old City. But he is not an ambassador and the mission is a consulate, not an embassy.

For decades, those distinctions have rankled many Israeli Jews. The United States, along with the rest of the world, has kept its primary diplomatic footprint not in Israel’s self-declared capital, Jerusalem, but in the commercial and cultural hub of Tel Aviv to avoid seeming to take sides in the fraught and never-ending argument over who really has the right to control this ancient city.

Until now. Maybe.

President-elect Donald J. Trump vowed during his campaign that he would relocate the mission “fairly quickly” after taking office. That in itself is nothing new: For years, candidates running for president have promised to move the embassy to Jerusalem, and for years, candidates who actually became president have opted against doing so.

But just as Mr. Trump broke all the rules of campaigning, some of his supporters say no amount of hand-wringing by the State Department will change his mind. Jason Greenblatt, an Orthodox lawyer who is advising Mr. Trump on Israel, told Army Radio after the election that the president-elect was “going to do it” because he was “a man who keeps his word.”