A new international music competition, the first designed to provide 20th-century. American composers the public hearing that has eluded them at Prestigious contests elsewhere, will begin next fall at the Kennedy Center, officials of the Center and the Rockefeller Foundation announced yesterday.

The entire cost of the Kennedy Center-Rockefeller Foundation International Competition for Excellence in the Performance of American Music, expected to be about $200,000 the first year, will be borne by the foundation.

The contest, to be held the week of Sept. 11, 1978, will be for pianists, offering a first prize of $10,000; a second prize of $5,000; and a third prize of $3,000. Each of five semi-finalists not qualifying for the finals will receive $1,500. In subsequent years the contest will be for singers, for chamber music ensembles, and possibly other solo instruments.

In terms of each prizes, the new contest offers somewhat more than the Cliburn competition, the much publicized event held in Fort Worth, where prizes this year totaled $22,250. Among European contests, the 1978 QUeen ELizabeth in Brussels one of the most prestigious is offering cash prizes totaling $33,000. The Leeds, in England, another major tourney, is putting up about $13,800.

The principal difference between the new Kennedy Center-Rockefeller competition and all others is in the emphasis placed on the American repertoire. In each KC-RF competition, contestants will be required to perform recital programs of which more than half is American music written after 1900.

About $22,000 has been spent by the foundation to make available scores of this music, little of which is known outside this country, and some of which has been out of print for years. The foundation and the center have distributed 200 sets of suggested works to music schools around the world.

Another $35,000 will be made available for managers in this country who engage the winners of the competitions. This extra sum is compensate for possible losses at the box office, where sales are said to slump when American music is programmed.

In addtion, a further prize of $5,000 may be awarded to a prize winner who, for a second season of concerts, agrees to repeat the programming of American music.

The first contest is open to every pianist, regardless of sex, age, or nationality. Ten thousand brochures, announcing the rules of the competition in English, Russian, French, Spanish, and German, have been sent to more than 1,900 conservatories and libraries throughout the world.

While the emphasis in the competition is on American music, the judging in the finals will be based on the excellence of the total program presented.

The announcement of the new Kennedy Center-Rockefeller Foundation Competitions comes to two weeks after the Center's announcement of the Friedheim Awards to American composers, also to begin in 1978. Washington has been the site of the J. S. Bach International Competition since the late 1950s that event has drawn contestants from as far away as Malaya, Turkey, Australia and Israel.