WARSAW—President Trump’s son-in-law and senior adviser, Jared Kushner, said that a show of unity among Israeli and Arab officials at a U.S.-backed conference here made him feel “optimistic” about prospects for peace in the Middle East, according to officials who witnessed the presentation behind closed doors on Thursday.

But Mr. Kushner provided no details of the Trump administration’s peace plan, which he has been developing for more than two years, the officials said. Mr. Kushner said in public comments later Thursday that...