The board of the New National Theatre Inc. yesterday appointed two of its members to a negotiating team in an attempt to resolve the continuing differences with the New York-based Shubert Organization, which books the theater.

Don Murphy, first vice president, and Joseph Fontana, counsel, have been instructed to negotiate "withdrawal" of the Shuberts from the partnership or "a more favorable contract that would reflect financial advantages" to the NNTI, according to Maurice B. Tobin, president of the board.

In a letter sent to board members on Wednesday, Bernard Jacobs, president of the Shubert Organization, accused Tobin of "intolerable interference with effective management of the Theatre" and challenged his "efforts to effect a unilateral closing of the Theatre." Yesterday, Tobin called that letter "knowing alarmism" on the Shuberts' part, calculated to pressure his board. "They want us out of the way so this can be a Shubert house."

In the letter, Jacobs also asked to meet directly with the National's board later this month to air mutual problems. Tobin said the board rejected that demand, agreeing to a face-to-face meeting only "when the negotiation phase has been fully exhausted."

Noting that he had only heard reports of yesterday's meeting from individual board members, Jacobs said yesterday that "the Shuberts are determined to stay at the National in accordance with the terms of our contract. We are sick and tired of Tobin's denigration of the Shubert Organization and are resolved to take no more nonsense from him."

As early as September 1981, just prior to the opening of "Evita," Jacobs said, the Shuberts did envision terminating their management contract with the National. But that proposal stemmed from "the frustrations" of dealing with Tobin. "Upon further consideration, we concluded it would be unfair to the community and ourselves not to fulfill our responsibility to the National," he added.

The differences between the two sides are aggravated by construction on a neighboring hotel and office complex, which has caused damage to the National Theatre. Reports vary on the seriousness--Tobin claims the National needs urgent repairs; the Shuberts and the Pennsylvania Avenue Development Corp. counter that it is safe for theater-goers.