WASHINGTON—The Trump administration is hammering out a compromise on auto-industry rules at the center of the North American Free Trade Agreement, increasing the chances that the U.S., Mexico and Canada can reach a deal this spring to revise the pact.

Canadian and Mexican officials have complained in recent weeks that the Trump administration has pushed for a quick resolution to Nafta talks—without showing flexibility on contested U.S. proposals designed to protect American jobs and balance trade within the bloc.

But...