Intensifying pressure for a swift end to the coal strike, President Carter appealed publicly yesterday to the coal industry and United Mine Workers to continue nonstop bargaining until a settlement is reached.

Carter's new exercise in labor-management jawboning came as industry negotiators relaxed their hard-line adherence to a previously rejected settlement and made several concessions, abandoning proposed fines for participation in wildcat strikes and restoring automatic cost-of living pay increases.

The union's bargaining council was reportedly holding out for more extensive concessions, however, and talks proceed into the night at the Labor Department here.

In opening a nationally televised news conference in Cranston, R.I., part of a political swing through New England, Carter said the country is "suffering already" from the 74-day coal field walkout and cannot afford another week of fruitless negotiations.

He said he hoped the strike could be settled "within the next few hours or a day or so" and warned again of "more serious action" - presumably meaning a back-to-work order under the Taft-Hartley Act - if the current negotiation efforts are not successful.

Carter told reporters he had just talked to Labor Secretary Ray Marshall and understood the bargainers were "making good progress" after all-night talks that included a secret Marshall meeting, between 2:30 a.m. and 5 a.m., with top U.S. Steel Corp. and Consolidation Coal Co. executives at the White House.

Sources said the corporate executives were J. Bruce Johnston, U.S. Steel's vice president and general manager for employe relations, and Bobby Ray Brown, president and chief operating officer of Consolidation Coal. U.S. Steel is a major "captive mine" owner - consuming all the output of its mines - and a dominant force in the Bituminous Coal Operators Association, the coal industry's bargaining group.

Thursday's round-the-clock talks resulted in yesterday's concessions.

Industry bargainers dropped their insistence on fines of up to $20 a day for participation in wildcat work stoppages, although they continued to demand disciplinary action against strike instigators and those who refuse to cross unauthorized picket lines.

Industry's agreement to retain exising cost-of-living increases would result in a total prospective three-year wage increase of $2.45 an hour instead of the previously proposed $2.35. The current hourly wage is $7.80.

The 39-member UMW bargaining council triggered the current impasse last Sunday by overwhelmingly rejecting a proposed settlement worked out earlier between BCOA and UMW President Arnold Miller that included a 37 percent wages-and-benefits increase over three years. The council had balked at the wildcat strike curbs, health benefit cuts, vacation modifications, production incentives and other labor-stabilizing and cost-cutting measures.

Marshall, with only two hours of sleep, met all day yesterday with union negotiators and bargaining council members who were brought to the Labor Department Thursday night in an attempt to involve them in the talks and thus prevent another contract rejection.

Industry bargainers were standing by on call from Marshall as the council, composed of the unions' top national and regional officials, debated the latest industry offer.

Bargaining council approval of a settlement would signal the start of a rank-and-file ratification process that could end the strike in 10 days and have coal moving to energy-starved midwestern and mid-Atlantic states by early March. Government and industry officials have said it would be two to three weeks before full coal production is resumed.

At his press conference, Carter said he believes the negotiators "recognize that there is a tremendous responsibility on their shoulders." He said "the future of the unions, the future of an effective collective bargaining process, the future of the coal industry and the welfare of our nation depends upon the success of these negotiations."

Avoiding criticism of the negotiators, the president said he believes they were bargaining "in good faith" and joined him in wanting to "avoid the necessity of me as president to take more serious action if the bargaining process is not effective." Said Carter: "the whole nation is looking at them with hope and confidence."

Carter earlier said he was considering invoking the Taft-Hartley Act to seek an injunction ordering the 160,000 strikers back to work for an 80-day cooling-off period. He confirmed in an interview Thursday that standby Taft-Hartley preparations were being made.

As full-scale talks resumed Thursday morning under a summons from Carter, Marshall had imposed a flexible two-day deadline, which would run out early today.

Carter's comments indicated the deadline could be stretched some but not much. Asked if the talks could drag on a week more, Carter said, "No, I don't think we could afford another week of negotiations. I would hope that we could conclude the negotiations within the next few hours or a day or so."

(Meanwhile, dwindling coal stock-piles in the Midwest and Northeast continued to plague electric utilities and their customers.

(Associated Press reported that state troopers and National Guardsmen escorted convoys of coal trucks to generating plants in Illinois, Indiana and Ohio, where nonessential power usage is better cut back and widespread job layoffs are threatened.

(In Springfield, Ill., 200 striking miners protested the arrival of non-union coal at the city's power plant, but 80 policemen kept the situation peaceful.

(Two non-union mines in Ohio agreed to close after authorities negotiated between the firms and 300 striking miners. One of the mine companies said it would continue to supply coal to hospitals and homes.

(Some 400 auto workers worked their last shift at a Chrysler Corp. plant in Southwest Indiana because of the electricity cutbacks, and the state's biggest utility. Public Service Indiana, said that beginning Monday schools and residents would have to cut their usage by 50 percent and 15 percent, respectively.

(Indiana residents, facing possible mandatory electric cutbacks next week, were buying out supplies of campstoves, lanterns, candles and batteries. "We've been out of oil lamps since last weekend, and I don't think you could find any more lamp oil to buy," said a Mishawaka hardware store manager.

(The dollar came under renewed pressure on foreign exchange markets, and dealers in London said the decline stemmed from the coal strike and concern over U.S. industrial performance and employment.)

Locally, acting Gov. Blair Lee said yesterday he will probably order mandatory electricity conservation in western Maryland next week because of dwindling coal supplies. He said Virginia Gov. John Dalton has asked for a meeting of the two states and West Virginia next Tuesday to consider energy conservation in areas served by Potomac Edison Co.