President Trump landed in Israel on Monday morning minutes after the first of 20 hostages were released by Hamas, and spent the day basking in the applause of a country that credits him, more than Prime Minister Benjamin Netanyahu, for joyous family reunions and a cease-fire after two years of war.

Mr. Trump seized on the moment to tell the Knesset, Israel’s parliament, that this is “not only the end of a war, this is the end of the age of terror and death.” Using a line that other presidents have reached for — and often been disappointed — he added: “This is the historic dawn of a new Middle East.”

Rarely has an American president, particularly one as divisive at home as Mr. Trump is, been met with such adulation abroad. In Hostages Square, tens of thousands yelled, “Trump, Trump,” and in the Knesset some members wore red MAGA-style hats.

Mr. Netanyahu, whose name was booed in the same square on Saturday night, declared the president was “the greatest friend that Israel has ever had in the White House.” There was more talk of nominating him for the Nobel Peace Prize and the Israel Prize.

And Mr. Trump himself surprised Israeli lawmakers when he twice made an offer to Iran — a country that Israel and the United States bombed only four months ago — to enter talks that could end decades of enmity and isolation.