WASHINGTON—President Donald Trump on Wednesday threatened to cut American aid to countries that back a United Nations resolution faulting the recent U.S. decision to declare Jerusalem Israel’s capital.

“We’re watching those votes,” Mr. Trump said at the start of a meeting of his cabinet on Wednesday. “Let them vote against us—we’ll save a lot. We don’t care.”

The U.N. General Assembly will meet Thursday in an emergency session to vote on a measure the U.S. blocked earlier this week at the Security Council, which called on the Trump administration to rescind its decision to move the embassy and recognize Jerusalem as the capital. The measure had the support of all other members of the Security Council, including U.S. allies France and the U.K.

U.S. Ambassador to the U.N. Nikki Haley said Tuesday evening that the U.S. “will be taking names” at Thursday’s General Assembly vote.

“We don’t expect those we’ve helped to target us,” Ms. Haley said on Twitter.