Mr. Trump’s announcement, on the eve of the NATO summit, could give the president a chance to take a victory lap at the gathering — if the truce holds. The timing of it had caught some of his own officials by surprise, and both sides continued to trade fire in the last moments before confirming a truce was in effect.

The Israeli military said it had struck missile launchers in western Iran that were poised to fire at Israel. Iran launched at least four barrages of ballistic missiles at Israel, setting off sirens that sent millions of Israelis rushing in and out of shelters. At least four people were killed when a missile hit an apartment building in the southern city of Beersheba.

But by around 7.30 a.m. in Israel, a tentative calm appeared to have taken hold as the military issued an all-clear, allowing people to exit bomb shelters. Soon after, President Trump announced the truce was in force. “PLEASE DO NOT VIOLATE IT!” he added.

There was initially silence from the Israeli government, which has in the past often waited in the first, delicate hours to see whether quiet is being answered with quiet before declaring conflicts over. Just after 9 a.m. local time, Israel’s government issued a statement saying it had agreed to a mutual cease-fire, having achieved its goals in its campaign in Iran, “and in full coordination with President Trump.” Iran, similarly, cast the truce as a sign its military had prevailed.

But underscoring the fragility of the situation, more sirens wailed in northern Israel nearly two hours later, warning of missiles launched from Iran. The Israeli military accused Iran of breaking the cease-fire — saying in a statement that it would “respond with force.”