The auto industry is juggling a range of policy priorities in Washington, from tariffs to tailpipe emissions. But one item remains firm atop President Donald Trump’s agenda for the industry: more jobs for Rust Belt states that helped elect him.

Mr. Trump made clear at a White House meeting Friday with top auto-industry executives that he wasn’t done prodding them on jobs—including foreign manufacturers. During a televised portion of the meeting, Mr. Trump told the executives he wants to see “manufacturing of millions of more...