The Carter administration has become embroiled in a bureaucratic skirmish pitting Energy Secretary James R. Schlesinger Jr. against Interior Secretary Cecil D. Andrus and Environmental Protection Agency head Douglas Costle over whether clear air rules should be weakened to allow the burning of more coal.

At issue is a controversial stand taken by Schlesinger early this month, when DOE dropped out of an interagency task force that had been charged with sending the president a unified report on how to increase domestic coal use.

Schlesinger instead sent a June 4 memo to President Carter urging him to call for amendment to the Clean Air Act.

Outraged, both Andrus and Costle sent memos to the president urging against Schlesinger's position.

Yesterday a senior administration official said the president had yet to review the memos. Copies have been leaked to the press by both sides. Schlesinger's 12-page June 4 memo was printed in yesterday's Congressional Record.

"I have never been involved in anything like this before," an EPA official remarked, adding, "Schlesinger's memo is misleading and incorrect."

"DOE has simply come out against clean ar," an Interior official said.

From the Forrestal Building, a DOE spokesman said that the task force would regroup and even issue a "final report," but that the "operative language could be found in Schlesinger's memo."

The major target of Schlesinger's opponents is his recommendation that utilities be allowed to use intermittent controls and improved monitoring systems to meet clean air regulations, instead of building costly exhaust scrubbers to remove pollutants.

"Intermittent controls," for example, would allow utilities to burn coal emitting sulfur dioxide and other pollutants on days when the wind conditions would limit the spread of emissions.

Schlesinger's memo argues that "without greatly expanded use of coal, this country may not make it" through the 1980s.

Andrus' memo to the president countered Schlesinger's arguments for intermittent controls, saying, "No date or information currently exists which would indicate [They] . . . would have more than a marginal effect on increasing demand for coal."

Sen. Edmund S. Muskie (D-Maine), a vigorous advocate of clear air rules some years ago, says intermittent controls are "the rhythm method of pollution controls and about as effective," and would likely lead Senate opposition to weakening existing rules.

Despite President Carter's 1977 goal of doubling coal production by 1985, Schlesinger wrote that the growth in domestic coal consumption is lagging. Instead of the 2 percent or less growth in coal use over the last five years, Schlesinger said a 4.5 percent annual growth target is necessary.

As expected, Schlesinger's stand was applauded by the coal industry. National Coal Association President Carl Bagge yesterday said the DOE memo "is blunt and unaccommodating, and has the merit of being true." He added that it is "the first hopeful sign from this administration."

Environmentalists roundly condemned the Energy Department's stance.

Louise Dunlap, head of the Environmental Policy Center, said, "Schlesinger is declaring war on the Clean Air Act and Strip Mining Act. It's also a sign we have two governments in the Carter administration."

Schlesinger's other recommendations to the president included:

Providing tax credits and a depreciation allowance to stimulate coal boiler construction.

Establishing "a one-stop" licensing system for coal-burning power plants and having states set aside plant sites.

Using strip-mine regulations in a fashion that "facilitates increased coal production."