In the days before a late-2016 vote on a United Nations resolution that criticized Israel, then-President-elect Donald Trump and top aides made a last-ditch push to target a majority of the U.N. Security Council to scuttle the text, people familiar with the situation said.

The lobbying effort, which ultimately failed, was wider and more intense than has been reported, according to interviews with dozens of diplomats and U.S. officials. It was also conducted against the wishes of the sitting U.S. government. The Obama administration’s...