President Carter invoked the Taft-Hartley Act yesterday in an attempt to force the rebllious United Mine Workers back to work and end the nation's record 91-day-old coal strike.

Declaring "the country cannot afford to wait any longer," he vowed to enforce emergency strike-ending provisions of the law despite widespread threars by many of the 160,000 strikers to defy a Taft-Hartley injunction against continuation of the walkout.

"The law will be enforced," he said, although administration officials conceded that, while courts can fine and imprison strike leaders, they are powerless to force individual miners back to work against their will.

Carter's long-threatened but often delayed direct intervention in the coal strike not only posed a challenge to the miners but represented a severe test of his leadership and the administration's economic and energy programs.

In a grim-faced appearance on national television, Carter said over-whelming rank-and-file rejection last weekend of a negotiated coal contract created a bargaining impasse that threatens to make the country "the innocent victim of a total breakdown of the collective-bargaining process."

Consequently, he said, he had appointed a three-member board of inquire to initiate the Traft-Hartly process and instructed Attorney General Griffin B.Bell to prepare to seek an injuction ordering the miners back to work for an 80-day cooling-off period.

Sources close to Carter said a temporary restraining order, the first step toward an injunction, will be sought as early as Thursday.

This could get miners back to work within days and coal moving again within a week or two, thus avoiding massive power cutbacks and job lay-offs expected to hit the East and Midwest if the strike continues.

But this scenario assumes substan- tial compliance with an injunction, a dubious assumption in light of the rumbles of the defiance out of the coal-fields and the miners' history of defying injunctions and traditional war cry that coal can't be "mined with bayonets."

Implicitly acknowledging it may take more than presidential declarations and court orders to get the angry miners back to work, Carter also said he would seek pay increases - raising average hourly wages from $7.80 to $8.80 immediately - for miners who return to work.

This is what they would have gotten under the contract they rejected for reasons other than wages, principally because of its provisions for health-care deductibles, wildcat strike and absenteeism controls, and other disciplinary measures sought by industry. Normally, injunctions mean returning to work under preexisting pay levels.

Although reportedly angry at Carter's suggestions of unilateral industry concessions, the Bituminous Coal Operators Association, the main industry bargaining group, agreed late yesterday to make the proposed $1-an-hour wage increase retroactive to the date the miners return to work so long as a new contract is negotiated and ratified before the Taft-Hartley injunction would expire, presumably in late May.

BCOA which includes 130 companies accounting for roughly half the nation's coal production, also indicated it would return to negotiations if the UMW could "assure BCOA negotiators and the nation that any new contract recommended by that team will be acceptable to the membership."

This is not precisely what Carter suggested, and it was not clear whether it would have any effect in getting miners back to work.

UMW President Arnold Miller, who predicted earlier that government action would "cause some violence in the coalfields." said yesterday he would obey an injunction. But the miners' 2-to-1 rejection of the proposed contract over the weekend represented a conclusive repudiation of his crumbling command of the union, and the statement was not viewed as a sign of rank-and-file compliance.

Taft-Hartley's main weapon against defiance is contempt-of-court fines and imprisonment, and administration officials said yesterday that fines would be assessed against local as well as national leaders of the union.

The national union treasury is virtually broke, but fines against locals would strike at the heart of the union, or at least whatever is left of the once-proud fiefdom of the late John L. Lewis and what he used to call the "shock troops" of the American labor movement.

In one of the three occasions when Taft-Hartely was invoked against the UMW during post-World War II coalfield turmiol, fines were levied totaling $1.4 million against the union and $20,000 against Lewis, although they were reduced later.

It is not only the union that was threatened by Carter's action yesterday, however. Administration officials said that Carter, by declaring a bargaining impasse - a move some lawyers said he many lack the precise legal power to do - was opening the way for company-by-company negotiations rather than the kind of industrywide settlement that has been in force since 1950.

This might, in effect, break up the BCOA while continuing the UMW on a local or regional level.

According to one theory, this could lead to scattered settlements that, combined with heavy production of nonunion coal and the eventual arrival of warmer weather, might enable the government to outlast the UMW and recalcitran coal operators.

One administration official said some coal companies are anxious to settle separately, and it was learned that the administration is encouraging that tren. As of last night, it was not known whether his gambit was succeeding, and officials indicated the didn't know whehter it would.

In opting for Taft-Hartley alon, Carter rejected his earlier plan to combine it with a request for congressional action authorizing temporary government seizure of the mines - a threst that President Truman used with success against the UMW in 1950.

"We have no plans to resort to seizure," said a top Carter aide after the president's announcement.

seizure was used as a threat to win BCOA agreement to the proposed contract 10 days ago, but was ruled out now for several reasons, officials said.

For on thing, it would be viewed as punitive against the industry, whereas the blame for the contract collapse laid with the union, they said. secondly, miners were considered unlikely to go back to work under an injunction if they could get better conditions under government seizure - which happened during past seizures and which many miners apparently thought would happen when they voted down the contract proposal last weekend. Thirdly, it might inhibit company-by-company settlements. Finally, it would put the government in the position of negotiating with the divided, unpredictable UMW, which a Carter aide described as "not preferable under any circumstances."

In his 10-minute statement, delivered in solemn tones from the White House press briefing room, Carter said the coal supplies have been reduced to a "critical level throughout the Midwest," with "tens of thousands of people" out of work.

"My responsibility," he said, "is to protect the health and safety of the American public, and I intend to do so."

He said he had asked the attorney general and the governors of coal-mining states "to make certain that the law is obeyed, that violence is prevented and that lives and property are fully protected."

Appealing to the miners' ethic of hard work and dedication, just as he did in his speech 10 days ago urging contract ratification, Carter said:

"As president, I call on the mine workers, the coal mine operators and all Americans to join in a common effort under the law to protect our country, ot preserve the health and safety of our people, and to resolve fairly the differences which have already caused so much suffering and division in our land."

The Taft-Hartley Act, passed in 1947 over President Truman's veto, has been invoked 34 times, with injunctions requested in 30 cases and granted in all but one: when President Nixon sought one against 200 grain elevator employes in Chicago. The act was last invoked by Nixon in 1971 in a dockworkers' dispute.

The law empowers the president to seek - and any U.S. District Court judge to grant - an injunction whenever a work stoppage is found to "imperil the national health or safety."

Before seeking the injunction, the president is required to appoint a board of inquiry to report on the strike. Carter yesterday named Carl A. Warns of Kentucky, Eva Robins of New York and John N. Gentry of Washington, all professional labor-management abritrators, to the board in the current dispute.

Gentry, chairman of the board, said about 5,000 Mailgrams had been sent to union and industry officials as well as other interested parties, inviting them to testify before the board.

The board met late yesterday in Labor Secretary Ray Marshall's conference room and was scheduled to reume deliberations today, with a hearing set for tomorrow. Administration officials said Carter asked for the board to report within 72 hours, which could take the Justice Department into court with a restraining order request by late Thursday.

Officials said the defendants could number in the thousands, including all UMW officials and mine operators affecttd by the strike, and noted that the government might have to go into as many as eight federal courts to assure that all affected mines and miners were covered.

After an injunction is granted, the Federal Mediation and Conciliation Service would try to bring the two sides to a negotiated settlement.

If there is no settlement after 60 days of the 80 day injunction period, the board of inquiry would reconvene and report the industry's last contract offer. This would be submitted to rank-and-file miners for ratification. Approval would mean the end of the strike; rejection would mean the miners were free to resume striking. At this point, the president is required to submit a report to Congress, raising the possibility of a legislated settlement.