JERUSALEM — There were warnings of a new Palestinian uprising and calls for protests at United States embassies, dire predictions that hopes for peace would be dashed irretrievably — and expressions of relief from Israelis who have waited a half-century for the world to remove the asterisk next to this city’s name.

Yet on the whole, the responses in the region to reports that President Trump will recognize Jerusalem as the capital of Israel — something no president has done in the nearly 70 years since Israel’s founding — remained hedged, if not entirely restrained, on Saturday. Arabs and Israelis alike were impatient to see whether Mr. Trump would really do it, precisely how he would define Jerusalem, and what else he might say or do to qualify the change.

Mr. Trump’s announcement, expected in a speech on Wednesday, would amount to the not-quite fulfillment of a campaign promise to move the United States Embassy to Jerusalem from Tel Aviv, a step for which many of Mr. Trump’s Jewish and evangelical supporters, and their allies in the Israeli right wing, have been clamoring.

For Israelis, it would acknowledge the obvious: that their government sits in Jerusalem, mainly on its western side — though the United States, along with the rest of the world, has not recognized the Holy City as Israeli territory, particularly since the Arab-Israeli War of 1967, when Israel conquered East Jerusalem.