Martin Feinstein, who has served as president and chief operating officer of the National Symphony Orchestra for the past 11 months -- while also holding the post of general director of the Washington Opera -- yesterday announced that his tenure with the orchestra would end as of Jan 2, 1981.

A statement issued jointly by Feinstein and Leonard Silverstein, chairman of the NSO association, said, "The scope and magnitude of the problems currently facing the National Symphony Orchestra, including the scope of its national support, require the attention of a full-time president. Mr. Feinstein, who also serves as general director of the Washington Opera, felt that it would not be feasible for him to serve in that capacity for the orchestra."

It is known that the orchestra's board of directors has felt for some time that its adequate management demands a full-time president. They had wanted Feinstein to quit his position with the opera to manage the NSO full-time; but given a choice, Feinstein chose the Opera.

Feinstein, who served for seven years as the Kennedy Center's executive director of performing arts, yesterday expressed admiration for the accomplishment of the NSO board of directors during his term as president and referred specifically to the recent million-dollar federal matching grant as a remarkable achievement. The orchestra has been experiencing serious financial problems, and Feinstein declared recently, "We're fighting for our life."

Yesterday Silverstein expressed gratitude "for Feinstein's unique contribution to the orchestra's well-being during 1980," and admiration for his "great impresarial ability." During the year he was president, the orchestra made highly successful tours of Japan and South America.

Feinstein declined any further comment on the resignation yesterday. NSO musical director Mstislav Rostropovich, who is in Europe, could not be reached.

Silverstein said yesterday that a nationwide search for a full-time president will begin immediately. At the same time, Robert J. Noerr, manager of the NSO since January 1972, was promoted effective immediately to the position of general manager.