The Obama administration set the higher mileage standards in an effort to reduce tailpipe emissions and combat climate change, and as a means of reducing the country’s dependence on foreign oil. Even if those targets are relaxed, the automakers will still need to comply with emissions rules set by California and several other states with tougher standards than the E.P.A.’s.

New fuel-economy targets were set in 2012 in an agreement reached by the Obama administration and automakers. The rule calls for steady increases in mileage, varying depending on the size of the vehicle and whether it is classified as a car or a light truck. The 2017 requirement for a large car is 33 miles per gallon, or about 25 miles per gallon in real-world driving. Most automakers meet or are close to this year’s goals, but they say the additional gains required through 2025 will be harder to achieve.

While the automakers would all prefer more lenient targets than the 2025 ones, they differ on the specifics. Some have invested heavily in new technologies and would prefer to have the standards continue to rise, albeit more modestly, to help ensure a market for their advanced vehicles. Honda, Hyundai and Toyota are planning a range of hybrids, electric vehicles and cars powered by hydrogen fuel cells to sell within a few years.

Others, such as Fiat Chrysler, have a lineup heavy on trucks and S.U.V.s and would be better off with a significant rollback in fuel-economy requirements.

The letters from the manufacturer lobbying groups represent the latest push by carmakers for a reprieve from the emissions and fuel-economy standards. This month, 18 auto-company chief executives wrote a letter to Mr. Trump on the same issue.

During the presidential campaign, on Twitter and in campaign stops, Mr. Trump heavily criticized automakers, especially Ford, for investing in Mexico. He has also threatened to impose a border tax on imports from Mexico, where many cars sold in the American market are made, especially smaller, less profitable models.

But after the election, the president and automakers became more closely aligned. Ford won praise from Mr. Trump after it announced it was canceling plans to build a new plant in Mexico. Other automakers have also announced plans to add jobs and invest in the United States.