UNITED NATIONS — In a heated session of the United Nations Security Council that appeared to serve little but to reinforce intractable divisions between Israelis and Palestinians, the Palestinian president, Mahmoud Abbas, accused Israel of acting like “a state above the law,” before Israel’s ambassador said that Mr. Abbas was “part of the problem.”

Amid the name-calling, no one seemed to acknowledge the surprise presence of Jared Kushner, President Trump’s son-in-law and adviser, who sat quietly with the American delegation in the Security Council chamber. Mr. Trump has charged him with forging “the ultimate deal” between the Israelis and Palestinians, though there has been little movement on that front.

Mr. Abbas was appearing before the Security Council for only the second time, after a 2011 visit in which he advocated Palestinian statehood. In his remarks on Tuesday, Mr. Abbas expressed an “absolute readiness to reach a historic peace agreement,” but said the United States had “not clarified its position.” For his part, the Israeli ambassador, Danny Danon, praised the Trump administration for “working very hard to make progress toward peace.”

Mr. Kushner was joined in the Council chamber by Jason D. Greenblatt, Mr. Trump’s Middle East envoy, with whom he is said to be drafting a peace proposal.