Barely a year old, the management agreement between the nonprofit New National Theatre Corp., which governs the National Theatre, and the New York-based Shubert Organization, which books the venerable playhouse, is showing severe signs of strain.

Maurice B. Tobin, president of the board, charged yesterday that the Shuberts are withholding critical operating funds due the theater, and said he had given them until mid-November "to settle up back accounts." He added that he was speaking with two other theatrical organizations about booking the theater if the dispute is not resolved.

The Shuberts immediately dismissed Tobin's charges as "an outright lie" and did not wish to make "any further statements that would be divisive at this time."

Ironically, the disagreement, also involving such matters as opening night parties and personnel, have come at a time when the National has one of the strongest bookings in its history, the musical "Evita," which opened Thursday night to a $1.4 million advance. But a report by two executives of the corporation indicates that the National's coffers are nearly empty due to "excessive" spending.

According to the contract between the two parties, the Shubert Organization pays, in addition to rent, $100,000 annually in quarterly payments to the New National Theatre Corp. Also, any profits earned by the theater are to be divided on a 50-50 basis.

Tobin claimed yesterday that the Shuberts have come forth with only $89,000 of last season's $100,000 payment and that there has been no accounting of the individual shows which played the National to determine the profits. "The theater has grossed $5.4 million so far," he said. "Shows like 'They're Playing Our Song' and 'Dancin' did enormously well at the National, and we haven't seen a piece of those profits. We've gone a whole year without a show-by-show accounting. Their the Shuberts' approach has been, we have 22 theaters, you're the 23rd. We'll get to it sooner or later.

"As a result, we've had to cancel some of our outreach programs -- "Monday Night at the National" and our children's theater -- and we've had to scale back "Noon at the National." If that's the case, we've been turned into a commercial theater, which jeopardizes us financially and also threatens our nonprofit status."

Tobin's charges were rejected vehemently by Bernard Jacobs and Gerald Schoenfeld, president and chairman, respectively, of the Shubert Organization. "Tobin can say whatever he pleases," said Jacobs. "The charge is absurd. . . . Our interest has always been the National Theatre and we think our record demonstrates it. What we wish to state is that any money due the National Theatre in accordance with the agreement has been paid.

"The one thing the Shuberts stand for is complete integrity of accounts," added Schoenfeld. "The record of the National is exemplary and exceeds that of the Shubert in Boston and the Forrest Theater in Phildelphia," both Shubert-run road houses.

Citing as an example "Amadeus," the Tony-winning drama that marked the beginning of the Shuberts' association with the National last fall, Jacobs said, "That show was a major contribution to Washington, but it lost $250,000 there. Still, we're very satisfied with the results. We felt that show enhanced the theater, and we believe that our continued presence there is a value to the town."

The rift has been further aggravated by a lingering dispute over who should pay the bill for the lavish opening-night party for "Amadeus," which cost $27,000, according to a source close to the theater. Tobin and The New National Theatre Corp. had initially planned to throw last Thursday's opening night party for "Evita" at the Corcoran Gallery of Art. In light of strained relations with the Shuberts, however, they pulled out at the last minute, even though invitations already had been printed. The affair, marked by acrimonious name-calling, was hosted instead by Robert Stigwood and David Land (producers of "Evita") and director Harold Prince at the Four Seasons Hotel.

Tobin defends the glittering opening-night parties as an essential component of the National's fund-raising efforts. Long an underdog to the Kennedy Center, the National has regained an image of glamor and excitement over the past season. But fund-raising has only brought in approximately $60,000, and the financial status of the New National Theatre Corp., according to a recent statement prepared by two board members, is "not good." The report noted that "we are spending at a rate approximately 2 1/2 times our income" and concluded, "Unless immediate steps are taken the NNTC will be unable to meet its obligations." The report also warned that the directors "could incur personal liabilities . . . We have known for some time that we are spending excessively."

The Shuberts and the NNTC also have been unable to find a mutually satisfactory theater manager to replace Richard Schneider, who left last month. And Tobin complained that the Shuberts' policy of closing the theater's bar on opening night has cut into revenues which he says are targeted for the children's theater program.

Tobin said that he will meet with the Shubert Organization on Oct. 9 in an attempt to iron out difficulties.