The Trump administration is backing away from a plan to freeze tailpipe-emissions targets for new vehicles through 2025, say people familiar with the process.

The administration is now considering requiring a 1.5% annual increase in fleetwide fuel efficiency, using an industry measure that takes both gas mileage and emissions reductions into account, the people said. The target moves the number closer to the Obama-era rules calling for 5% gains but still provides auto makers with significant relief and would allow cars to...