Rep. Martin Frost (D-Tex.) announced yesterday that he will not run for chairman of the House Budget Committee, a move that leaves Rep. William H. Gray III (D-Pa.) as the only declared candidate for the position.

The chairmanship was thrown open last month when House Democrats, meeting in caucus, voted against a rules change that would have allowed Rep. James R. Jones (D-Okla.) to remain as chairman.

House rules limit service on the committee to three terms and Jones has reached the limit. Without the rules change he and five other members will leave the committee in January.

Democrats will control the new House by a 69-seat margin (with one contest involving Indiana Democrat Frank McCloskey still unresolved) and therefore will select the committee chairmen.

The chairmanship of the Budget Committee has been one of the most influential posts in the House and likely will be so again next year with President Reagan expected to propose severe new budget cuts in an effort to reduce the federal deficit.

According to House Democrats, Frost, a moderate from the Dallas area, decided to back out of the race for the chairmanship after discovering that Gray had lined up enough commitments during the summer and fall.

In a statement released by his Capitol Hill office yesterday Frost said, "I have reviewed the situation and have concluded that the votes simply are not there . . . . It is apparent that my colleague, Congressman Bill Gray of Philadelphia, will be elected as the next chairman of the Budget Committee."

Gray, a Baptist minister and liberal who has earned a reputation as an effective coalition-builder in the House, said yesterday that Frost's announcement was "good news."

Only two weeks remain before the 99th Congress convenes and Democrats caucus to select committee chairmen.

"At this particular point I don't know of another candidate," Gray said. "Unless someone gets into the race I assume that on January 4 [the date of the caucus] I will be the only one nominated."

Gray, according to associates, has received commitments from about 160 House Democrats, including the Congressional Black Caucus, many liberals and a large group of southern conservatives, for whom Gray has campaigned in the past and with whom he has successfully worked in the past.