President Carter intervened unexpectedly in the 60-day-old coal strike yesterday in an attempt to avert disruption of fragile negotiations between the United Mine Workers and the coal industry.

In a departure from his hands-off policy toward the strike, Carter sent word to UMW President Arnold Miller urging a one-day postponement of a union bargaining council meeting that had been scheduled for 10 a.m.

The request was conveyed by Labor Secretary Ray Marshall in a phone call to Miller shortly before the meeting of the UMW's top regional officers was to have begun.

Miller agreed, and rescheduled the meeting for Tuesday. This gives the UMW and coal industry negotiatiors more time to hammer out a full contract package before Miller has to face the council, which must approve a contract before it is submitted to union members for ratification. One theory is that a fully balanced package would be easier to sell than fragments, including such controversial already apporoved provisions as penalties for wildcat strikes.

The meeting had been scheduled earlier in the week, when a settlement appeared imminent. But hopes faded late Thursday as the talks - conducted under heavy secrecy in the office of chief federal mediator Wayne L. Horvitz - produced no results.

Shortly after midnight, Horvitz suspended the talks for the rest of the night, saying an agreement was still beyond reach although the differences had "narrowed significantly." He said he waould not call it a break-off, although other administration sources said the situation appeared "bleak."

Horvitz indicated that the major hurdled continues to be money, including fringe benefits as well as wages.

Other sources said the union is holding out on money and certain other related issues in an effort to balance trade-offs it had to make to meet industry demands for labor stability in the mines, principally an end to the wildcat strikes that crippled Appalachian coal production last summer.

The tentatively agreed-upon labor stability clause calls for fining wildcat strikers to recoup losses to benefit funds caused by strike-related production interruptions. If an abritrator subsequently finds that an employer provoked the walkout, the employer would be ordered to reimburse miners for the fines.

After the intensive settlement drive Thursday, the talks shifted to low gear yesterday.

Horvitz met for several hours with Miller and his team, keeping in telephone contact with industry bargainers ensconced in the Capitol Hilton Hotel several blocks away from the Federal Mediation and Conciliation Service offices. By lat afternoon, Miller also left the offices reportedly bound for Charleston, W.Va., where he has frequently spent weekends during the talks.

Sources on both sides said they expected contacts to continue over the weekend, although another intensive settlement push might not come before Sunday or Monday. "With the bargaining council off till Tuesday, the pressure is off," said one resource.

Carter's move - his first overt involvement in the strike since it began Dec. 6 - came as rapidly dwindling coal stocks in Ohio and other key industrial states intensified political pressure for administration action to get the 160,000 striking miners back to work.

A bargaining collapse could trigger pressure for stronger action than the administration wants to take, including seeking a Taft- Hartley Act injunction to force the miners back to work.

Carter said at his news conference Monday he had "no present intention" of intervening in the strike. Labor Department officials said the meeting-delay request was not intervention in the old Lyndon Johnson sense of locking bargainers in the White House and twisting arms until a contract was signed. They said there are still no plans to seek an injunction.

Rep. William H. Harsha (R-Ohio) was the latest public official from a coal-dependent state to call for an injunction yesterday, saying it would be "unconscionable to allow this impass to continue." Earlier Ohio Gov. James A. Rhodes, also a Republican, called for Carter to bring the negotiations to the White House and assume the role of chief mediator.

A negotiated settlement would have to be approved by the union's bargaining council and the 160,000 strikers before the walkout ends, a process that could take 10 days or more. Another 10 days or two weeks would pass before the coalfields are back in production.