TEL AVIV—Israel’s prime minister on Saturday accused the Obama administration of a “shameful” act against his country after the U.S. helped pass a United Nations resolution that labels Jewish settlements illegal, saying it will only make it more difficult to negotiate peace with Palestinians.

The comments by Prime Minister Benjamin Netanyahu came a day after the White House broke from a longstanding tradition of defending Israel against censure by the U.N. Security Council. Palestinians, too, voiced skepticism that the resolution...