President Trump on Friday directed his administration to negotiate with California over a proposed rollback of fuel economy and tailpipe emissions standards, a move that could avert a damaging court battle with the potential to sow chaos in the auto industry.

California has vowed to disregard any rollbacks and stick to its own stricter emissions standards. Nonetheless, the state must be invited to the negotiating table as the administration moves forward with its plan to relax the fuel economy rules, Mr. Trump said at a White House meeting between top administration officials and major auto executives, according to three people briefed on the closed-door discussions.

Mr. Trump’s directive at the meeting grants a reprieve to automakers, who lobbied for a relaxation of rules aimed at cutting tailpipe emissions of carbon dioxide — a major contributor to global warming — but in recent weeks became increasingly nervous that the zealousness of the proposed rollbacks would provoke a battle with California.

It remains unclear whether administration officials and California can hope to reach a compromise.

The sides are far apart, and, given previous statements by Scott Pruitt, the Environmental Protection Agency head, it was unclear whether any negotiations would be “a good-faith engagement or for show,” said David Friedman, who served as acting administrator of the National Highway Traffic Safety Administration under President Barack Obama.