President Carter and Labor Secretary Ray Marshall said yesterday they believe rank-and-file members of the United Mine Workers will approve a tentative contract with the soft-coal industry and end the longest continuous coal strike in the nation's history.

The 83-day strike had idled 160,000 mine workers, prompted power cutbacks and threatened plant shutdowns and layoffs in the Midwestern industrial states.

"There's a good chance" that the striking miners will vote to return to work, Carter said yesterday after services at Washington's First Baptist Church, where he, Rosalynn Carter and other members of the congregation prayed for union ratification.

The tentative agreement was reached Friday night between the UMW and the Bituminous Coal Operators Association, the Industry bargaining group.

Marshall said he believes the contract will be approved because it is better than a separate but similar agreement with the Pittsburgh and Midway Coal Mining Co. that was rejected over the weekend by miners in Kansas, Missouri and Kentucky.

Many observers viewed the P&M rejection as an early indication of trouble for the larger UMW-BCOA accord. But Marshall said yesterday on "Face the Nation" (CBS, WTOP) he believes "the general agreement made between BCOA and United Mine Workers influenced the outcome in voting on the P&M contract."

He said the striking miners realized "the BCOA agreement was better for them and, therefore, they were less likely to accept the P&M agreement."

For example, the P&M contract did not guarantee funds for health and pension benefits but left that open pending a settlement with the BCOA. The BCOA contract guaranteed those funds, Marshall said. And since the UMW negotiators accepted the contract. "You would expect that that would be some indication of the ability of that agreement to succeed," Marshall said.

The UMW's "education campaign" began yesterday.

More than 200,000 copies of the agreement, reached under pressure from the White House and an increasingly edgy public, were sent to the coal fields yesterday.

"We're sending the copies by trucks, airplanes and any way we can get them to our members," UMW President Arnold Miller told the Associated Press. "I think the rank and file will accept this agreement once they see for themselves what's in it," he was quoted as saying. Miller has said he will take no part in the selling of the contract; he is very unpopular with much of the union's membership.

Marshall said the Carter administration would not participate in the "education campaign." It had been reported that some officials would publicly urge acceptance.

"This is a hands-off time for us be cause the decision is up to the miners, and that's the way it should be," he said. "Our basic objective was to try to get the dispute resolved with the contract. We thought that was better than any other alternative. Now that that objective has been achieved, we would let the democratic process take effect," Marshall said.

The administration had threatened to take "drastic" federal action, perhaps including seizure of the mines, if the UMW and industry negotiators had failed to reach an agreement by the weekend. The administration had been accused of pressuring the owners to settle.

Marshall saidyesterday that was not so.

"I can tell you that did not happen. . . I think there was pressure on all sides," he said.

And if the contract is not ratified?

"I don't know," said Marshall. "We'll have to cross that bridge when we come to it. It's obvious that a 'Yes' vote would be the best resolution of this." However, he cautioned that his comments should not be interpreted as an administration endorsement of the contract.