WASHINGTON—Former national security adviser Mike Flynn and others within the White House ignored repeated legal and ethical warnings as they pushed early in President Trump’s tenure a plan to build dozens of nuclear-power reactors in Saudi Arabia, according to a report by a House panel released on Tuesday.

After the House Committee on Oversight and Government Reform released the report, the Democratic-led panel said it was launching a formal investigation into the possible transfer of sensitive U.S. nuclear technology to Saudi...