On Thursday morning, a wider group of automakers held a meeting to consider joining the pact, the executive said, although there were no immediate sign-ons. Ford, Honda, BMW and Volkswagen had initially decided to keep the group small, he said, because a wider group would have been more difficult to bring together, raising the prospect that word would get out and the deal would collapse.

An executive at another large automaker said his company was considering joining the agreement because it included meaningful concessions by California. The executive, who spoke on condition that neither he nor his company be identified, said that the Obama-era fuel economy standards were difficult for the industry to meet because car buyers increasingly prefer sport utility vehicles and pickup trucks that tend to have much lower fuel economy than sedans.

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Margo Oge, a former senior E.P.A. official who worked on auto emissions policy and now serves as an informal adviser to several auto companies, said, “I have been calling all these companies and telling them to cut a deal with California. I think G.M. and Toyota will also have the courage to sign on.”

Trump administration officials said the California deal would not stop their plans to put forward a new federal rule to allow more tailpipe pollution. The deal “has no impact on E.P.A.’s regulation of greenhouse gas emissions under the Clean Air Act,” wrote Michael Abboud, an E.P.A. spokesman, in an email. “This voluntary framework is a PR stunt that does nothing to further the one national standard that will provide certainty and relief for American consumers.”

The new agreement would also give automakers more leeway in meeting the fuel economy standards through other means, like earning credits for fuel-saving technology.

Some environmental groups criticized the slower pace and expanded loopholes the deal awarded the automakers. “That means more pollution, less savings at the pump and a bad precedent for future standards,” said Daniel Becker, director of the Safe Climate Campaign at the Center for Auto Safety, a nonprofit group based in Washington.

The carmakers are addressing a crisis that is partly of their own making. Soon after Mr. Trump was elected, the chief executives of the United States’ Big Three auto companies — Ford, General Motors and Fiat Chrysler — met with Mr. Trump in the Oval Office and asked them to loosen the Obama emissions rules. But the automakers have since grown alarmed at the expanding scope of the administration’s plan.