President Carter expressed strong opposition yesterday to a Senate amendment giving the auto industry another five years to clean up pollution from its cars.

The President's letter was sent to Chairman Edmund S. Muskie (D-Maine) of the Environmental Pollution Subcommittee as the Senate began debate on a big clean air bill with dozens of lobbyists milling through the halls.

The deadline for auto cleanup is one of three key sections in the bill. A second is a section forbidding construction of new plants in areas which already have clean air if the effect would be "significiant deterioration" of the air quality in the region. The third has to do with a requirement that new plants which add pollution may not be built in "dirty-air" areas unless an equal amount of pollution is removed by closing or cleaning up some other source - perhaps an older, "dirtier" plant.

In 1970 Congress voted to require the auto industry to reduce pollution by 90 per cent - in comparison with cars then being built - by 1975-76. The industry has come part of the way and current new cars have 56 per cent less carbon monoxide and 63 per cent less hydrocarbon emissions than 1970 cars, as well as 38 per cent less emissions of oxides of nitrogen, according to a Muskie subcommittee report.

The auto companies, arguing that they can't meet the 90 per cent deadlines without a reduction of mileage and added cost, have already won postponements until 1978. Now they want them stretched out to 1982. The Muskie subcommittee bill, which Carter indicated he strongly prefers, gives them a stretch-out until 1980.

Carter, in his letter, said "More than 96 million people in at least 48 of our cities breathe air which exceeds the federal health-based air quality standards." He said he opposed the auto industry five-year stretchout, and also opposes an expected amendment to weaken the provisions against "significant deterioration" of air which is already cleaner than the levels set to protect health.

Carter included a letter from Transportation Secretary Brock Adams, Environmental Protection Administrator Douglas M. Costle and Federal Energy Administrator Jack O'Leary declaring that the Muskie subcommittee goals could be achieved with "little or no fuel economy penalty . . . if the industry employs the optimal fuel economy technology."

The five year stretchout provision was developed by the United Auto Workers union and has the backing of the AFL-CIO, the auto companies, the National Auto Dealers Association and the Automotive Service Industry Association, which deals in auto parts and which wants some existing provisions on pollution parts guarantees and services softened.

The union and the industry have never before this year put forward a strong coalition, and they have a good chance to win in the Senate. Their provision has already been adopted by the House, and is being sponsored in the Senate by Donald W. Riegle Jr. D-Mich.) and Robert P. Griffin (R-Mich.).

The National Clean Air Coalition, including groups like Friends of the Earth, Sierra Club, American Lung Association and local government groups, oppose Riegle.

Yesterday, amid considerable maneuvering, it appeard that Muskie and the administration might fall back on a compromise amendment being sponsored by Howard H. Baker Jr. (R-Tenn.) which less helpful to the industry than Riegle-Griffin, but gives the auto makers a bit more leeway than does the Muskie subcommittee version. Alternatively, some other compromise variation may be passed. A final vote on this issue could come today.

Yesterday, Sen. Gary W. Hart (D-Colo.) offered an amendment to beef up the Muskie requirements on nitrogen oxides and require a study of just how far such emmissions should be reduced. But the beef-up part was knocked out by Griffin, 51 to43, leaving only the study.