The economic logjam that had threatened the Vienna State Opera's planned appearance at the Kennedy Center has been broken. The company plans to travel to Washington in autumn of 1979 - about a year later than originally intended.

The resolution of the impasse, which arose when the Austrian government withdrew its portion of the costs of the visit in an austerity drive earlier this year, was disclosed yesterday by Fred Sinowatz, the Austrian minister of education and culture, in an interview.

Sinowatz said the decision to "push through" the visit of the celebrated company was made by Chancellor Bruno Kreisky. He said the chancellor had received communications from numerous Americans, asking that the appearance be salvaged, including a letter from former Secretary of State Henry Kissinger.

Close to $1 million in Austrian shillings has been released by the government to pay for most of the company's transportation. The rest of the expenses - labor and production costs, for instance - will be picked up by the Center.

This would be the first visit to the United States by the state opera, which is 108 years old. Performing 10 months a year and 7 days a week except holidays, it is the world's busiest opera company - and one of the best.

The Vienna Opera is to perform in Washington only. But the Vienna Philharmonic, which serves as pit orchestra for the opera, is to perform elsewhere in the country, as well as at the Kennedy Center Concert Hall. A source at the opera said that every effort will be made to duplicate the performances originally proposed for Washington. Among the high points were Beethoven's "Fedelio" under Leonard Bernstein, Strauss' "Ariadne auf Naxos" under Karl Bohm and Verdi's "Don Carlo" under Herbert von Karajan.

Artists who have been asked to hold dates open in 1973 for Washington appearances now will have to try to carve periods into their schedules a year later. Some schedules run as much as three and four years ahead.

The news of the $1 million allocation by the Austrian government came as a surprise yesterday to Martin Feinstein, executive director for the performing arts at the Kennedy Center. But after placing a call to Egon Seefehlner, the director of the Vienna Opera, Feinstein reported that although exact dates have yet to be worked out, he expected appearances to be scheduled for late summer or early autumn of 1979.

Feinstein plans to fly to Vienna in February or March to negotiate date and repertoire. He said it appeared that Leonard Bernstein would be free to conduct Beethoven's "Fidelio," as planned.

The financial crisis that led to' postponement of the visit was caused about six months ago by the Socialist Party leadership of Chancellor Kreisky. Faced with a deficit that had been steadily mounting ever since the Arab oil embargo, budget cuts were ordered across the board. This action hit the state opera particularly hard. That was because about $20 million, or 80 per cent of the opera's budget, comes from the federal treasury. The rest is from box-office receipts.

The opera, and its three sister performing-arts institutions that comprise the federal theater system, were at the time receiving a federal subsidy of about $55 million, from which they were ordered to cut $2.8 million. Since a substantial proportion of state revenues to the institutions were tied up in fixed costs such as pensions, which alone amounted to 25 per cent of expenditures, there was little flexibility.

The result was delay of the American visit and the driving up of costs for certain orchestra seats to levels unprecedented on any regular basis in the United States. Standard prices for major performers such as Karajan or Berstein now reach a top of at least $55 each, and in some cases considerably more. All the events planned for the Washington visit are in the high-price category, and that further complicated arrangements for the opera's journey.

An American source in Vienna pointed out that by delaying an expensive American visit by a year, the government could more easily ride out public protests about the ticket increases. Allowing the developments to coincide would be harder to handle for a socialist government in a country jealously guarding its unemployment rate of only 1.1 per cent.

While not among the oldest of opera companies, the state opera has a long history of excellence. Among its former directors are Gustav Mahler, Felix Weingartner, Richard Strauss, Clemens Krauss and both Bohm a nd Karajan.