The White House, blindsided by a pact between California and four automakers to oppose President Trump’s auto emissions rollbacks, has mounted an effort to prevent any more companies from joining the other side.

Toyota, Fiat Chrysler and General Motors were all summoned by a senior Trump adviser to a White House meeting last month where he pressed them to stand by the president’s own initiative, according to four people familiar with the talks.

But even as the White House was working to do this, it was losing ground. Yet another company, Mercedes-Benz, is preparing to join the four automakers already in the California agreement — Honda, Ford, Volkswagen and BMW — according to two people familiar with the German company’s plans.

Mr. Trump, described by three people as enraged by California’s deal, has demanded that his staff members step up the pace to complete his plan. His proposal, however, is directly at odds with the wishes of many automakers, which fear that the aggressive rollbacks will spark a legal battle between California and the federal government that could split the United States car market.

The administration’s efforts to weaken the Obama-era pollution rules could be rendered irrelevant if too many automakers join California before the Trump plan can be put into effect. That could imperil one of Mr. Trump’s most far-reaching rollbacks of climate-change policies.

The proposal would significantly weaken the 2012 vehicle pollution standards put in place by President Barack Obama, which remain the single largest policy enacted by the United States to reduce planet-warming carbon dioxide emissions. The Obama-era rules require automakers to nearly double the average fuel economy of new cars and trucks to 54.5 miles per gallon by 2025, cutting carbon dioxide pollution by about six billion tons over the lifetime of all the cars affected by the regulations, about the same amount the United States produces in a year.

Carbon dioxide in the atmosphere traps the sun’s heat and is a major contributor to climate change.

In addition to Mercedes-Benz, a sixth prominent automaker — one of the three summoned last month to the White House — intends to disregard the Trump proposal and stick to the current, stricter federal emissions standards for at least the next four years, according to executives at the company.

Together, the six manufacturers who so far plan not to adhere to the new Trump rules account for more than 40 percent of all cars sold in the United States.

“You get to a point where, if enough companies are with California, then what the Trump administration is doing is moot,” said Alan Krupnick, an economist with Resources for the Future, a nonpartisan energy and environment research organization.

A senior administration official said the California pact was an effort to force Americans to buy expensive vehicles that they don’t want or need. Speaking on condition of anonymity, he called the pact top-down policymaking with California trying to impose its standard on 49 other states.

Mr. Trump has billed his plan, which would freeze the standards at about 37 miles per gallon, as a deregulatory win for automakers that will keep down car prices for American consumers. Mr. Trump’s plan would also revoke the legal authority of California and other states to impose their own emissions standards.

In an extraordinary move, automakers have balked at Mr. Trump’s proposal, mainly because California and 13 other states plan to continue enforcing their current, stricter rules, and to sue the Trump administration. That could lead to a nightmare situation for automakers: Years of regulatory uncertainty and a United States auto market that effectively split.

Last week, California officials said that they expected more automakers to join their pact, which commits carmakers to build vehicles to a standard nearly as strict as the Obama-era rules that the president would like to weaken. “Many companies have told us — more than one or two — that they would sign up to the agreement as soon as they felt free to do so,” said Mary Nichols, the top clean air official in California.

Officials from Mercedes-Benz declined to comment.

Executives from the three auto companies summoned to the White House declined to comment publicly on their interactions with the Trump administration. But at a recent media event, Mike Manley, Fiat Chrysler’s chief executive, said of the California pact: “We are absolutely going to have a look at it and see what it means.”

In the Trump administration, three senior political officials working on the rollback, a complex legal and scientific process, have all left the administration recently. A senior career official with years of experience on vehicle pollution policy was transferred to another office.

That means the process is now being helmed by Francis Brooke, a 29-year-old White House aide with limited experience in climate change policy before moving over from Vice President Mike Pence’s office last year. Given the lack of experienced senior staff members, people working on the plan say it is unlikely to be completed before October.

At the same time, staff members at the Environmental Protection Agency and Transportation Department, which are writing the rule, say they are struggling to assemble a coherent technical and scientific analysis required by law to implement a rule change of this scope.

Several analyses by academics and consumer advocates have questioned administration’s claim of benefits to the public. An Aug. 7 report by Consumer Reports concluded that Mr. Trump’s proposed rollback would cost consumers $460 billion between vehicle model years 2021 and 2035, an average of $3,300 more per vehicle, in car prices and gasoline purchases. It also found the rollback would increase the nation’s oil consumption by 320 billion gallons.

A career staff member at the E.P.A., speaking on condition of anonymity, said the numbers, the public comments and the analysis were at odds with what the White House wanted to do.

The White House official called the staff departures irrelevant and said that the rule was near completion. While acknowledging that a major change such as this takes time, the official said that people who were opposed to the rule, including some in the automotive industry, were starting to worry that the Trump plan was going to succeed.

Policy experts point out that Mr. Trump’s quest to undo his predecessor’s signature climate-change regulation despite opposition from the very industry being regulated is extraordinarily unusual. For automakers, they say, it makes more sense to try to remain globally competitive by building more sophisticated vehicles as the world market moves toward more efficient cars.

“I don’t think there is any precedent for a major industry to say, ‘We are prepared to have a stronger regulation,’ and to have the White House say, ‘No, we know better,’” said William K. Reilly, who headed the E.P.A. in the first George Bush administration.

For some companies, Mr. Trump’s regulations are already moot. An E.P.A. assessment of the 2017 Honda CR-V, the best-selling S.U.V. in the country that year, showed the car is set to meet 2022 Obama-era targets five years ahead of schedule.

Late last month, in the days immediately after the deal between California and the four automakers was announced, White House discussions ranged widely about how to respond.

At one White House meeting, Mr. Trump went so far as to propose scrapping his own rollback plan and keeping the Obama regulations, while still revoking California’s legal authority to set its own standards, according to the three people familiar with the meeting. The president framed it as a way to retaliate against both California and the four automakers in California’s camp, those people said.