Rep. John D. Dingell (D-Mich.) and the auto industry yesterday agreed to support a compromise on auto emmission standards proposed by United Auto Workers President Leonard Woodcock.

Woodcock's proposed auto emission standards are not as stringent as those proposed by Sen. Gary W. Hart (D-Colo.) and Rep. Paul G. Rogers (D-Fla.), but they are not as lenient as the auto industry had been demanding through a bill Dingell has introduced.

An auto industry spokesman called the move a "concession to political reality," admitting that the chances for greatly relaxed standards had been hurt by the loss of a Republican in the White House who had backed the industry. The concession does not entirely settle the differences between the Hart and Rogers proposals and what the industry, backed by the UAW, wants in the way of revision of the Clean Air Act.

Bascially, Hart proposed giving the auto industry a one-year extension of the 1977 standards before tougher standards would go into effect.

Rogers, head of a House Commerce subcommittee on clean air, is willing to give the auto industry a two-year extension, but wants the act's standards met by 1980, except for nitrogen oxides, for which he would allow them one more year.

The auto industry and Woodcock had all along agreed on demanding a two-year extension of the 1977 standards, arguing that they could not meet the new standards required in 1978 under the act.

Where they had parted was on what should happen in model year 1980. Dingell and the auto industry wanted California's standards, the toughest in the nation, on emissions of hydrocarbons, carbon monoxide and nitrogen oxide to take effect nationwide for an interim period of two years.

Then, the Clean Air Act's tougher standards would be imposed for all but the nitrogen oxide emissions, the emission level of which would be set by the Enviromental Protection Agency.

The Woodcock compromise would require meeting the Clean Air Act's tougher standard in 1980 for hydrocarbon emissions, but only the California standard for carbon monoxide and a revised standard for nitrogen oxide in 1982.

Herbert L. Misch, vice president of environmental and safety engineering for the Ford Motor Co., said, "Although the emission levels proposed by [the UAW and Dingell] are more stringent than those previously supported by the Ford Motor Co., they do represent a realistic compromise which appears to be technically feasible."

Misch added, "The timetable does, however, generate the risk associated with premature application of advanced technology needed to meet the latter standards," a spokesman explained that meant the industry would have to adopt a new emissions control device before it was fully tested, although he admitted they were going to put the device on all models to be sold in California next year.

Rogers said the move meant Dingell and the industry were "coming closer to my position," and added that he had no intention of compromising further.

The Carter administration has endorsed a one-year extension, but has said nothing about what should happen after that.

Woodcock, in a news conference yesterday, said he had discussed the UAW's position with President Carter, energy chief James R. Schlesinger and Transportation Secretary Brock Adams, but had received "no specific response" except a promise to look into it.