JERUSALEM—Vice President Mike Pence vowed Monday that the U.S. will open its embassy in Jerusalem next year, but he signaled support for the resumption of talks toward an Israeli-Palestinian peace deal as the Palestinian leadership backed off a threat to abandon those negotiations.

In a speech to Israel’s Knesset, Mr. Pence sent dual messages. He cast the embassy move as an expression of the Trump administration’s unwavering support for Israel, drawing cheers when he formally announced the quick timetable and declared: “Jerusalem...