Negotiations to end the seven-week-old strike by the United Mine Workers broke off abruptly early yesterday, virtually assuring the nation its longest coal strike in decades.

The new deadlock came shortly after Republican Gov. James A. Rhodes of Ohio called on President Carter to take "positive federal action" to end the strike before electric utilities run out of coal.

Rhodes' appeal adds a political dimension to the strike that could test the Carter administration's hands-off policy toward labor disputes. Labor Secretary Ray Marshall said yesterday the administration still has no plans to seek an injunction to get the 160,000 UMW strikers back to work.

As of late yesterday, there were no immediate plans for resumption of the negotiations, though federal mediators were in touch with both sides in an attempt to create a climate for renewed bargaining.

The latest deadlock - the second in three weeks - came only hours after industry sources indicated optimistically that a tentative contrast settlement might be reached by the end of the week.

As the talks headed into their first night session since the strike began Dec. 6, the Bituminous Coal Operators Association the industry's bargaining group, made a "presentation" that was reportedly intended to be the basis of a settlement. But it was rejected by the union negotiators, and BCOA broke off the talks.

Things blew up around midnight and it was all over by 2 a.m.," said one source. Mediators made a futile attempt to patch things up and then left around 3 a.m. the sources said.

Sources on both sides indicated that no single issue precipitated the new stalemate, although wages - previously peripheral to the main stumbling blocks of benefit guarantees and production stability - reportedly played a part in the new impasse.

"They'd gotten to the point where everything had been discussed, and it was a question of putting a package together," said one source. Although a similar breakdown occurred late last month at a similarly critical stage, "this was a more serious attempt" to reach a settlement "and thus a more serious setback," the source said. The previous breakdown lasted nearly two weeks.