The Soviet Union made public yesterday an approving response to a proposal by two former U.S. admirals for a halt to all nuclear tests, beginning in August, but the sponsors said the reply "falls short of the firm commitment" they had requested.

Retired rear admiral Eugene J. Carroll Jr., deputy director of the Center for Defense Information, a Washington-based research organization, said he received a response Monday from Ambassador Anatoliy Dobrynin. An account of the response was made public yesterday by the official Soviet news agency, Tass, in a dispatch from Moscow.

Carroll said he and retired rear admiral Gene R. LaRoque, director of the research center, proposed to the Soviet Union Jan. 18 that it announce a moratorium on all nuclear weapons testing effective Aug. 6, the 40th anniversary of the first atomic bomb, dropped by the United States on Hiroshima, Japan. A similar proposal was made to President Reagan last year. The retired admirals recommended that the moratorium on testing be accompanied by resumption of negotiations on a comprehensive treaty banning nuclear tests.

The Soviet response, as delivered by Dobrynin, said a test moratorium and new negotiations on a comprehensive treaty "undoubtedly would contribute to constraining the nuclear arms race." The document noted that the Soviet Union previously had suggested a moratorium on all nuclear explosions, "beginning from a mutually agreed date."

The document added, "The date the moratorium would take effect could be, as you suggest, Aug. 6, 1985," or even earlier, if other nuclear powers agree. The Tass rendition seemed to go further, saying the Soviet Union "agrees that the moratorium goes into effect on Aug. 6, 1985," but such a definite statement is not contained in the document presented to Carroll.

The proposal to halt nuclear testing as of Aug. 6 was made public last year on the same date, according to Carroll, and presented in a letter to President Reagan on Nov. 27. Lt. Gen. John T. Chain Jr., State Department director of politico-military affairs, replied for Reagan on Dec. 31 in a letter that rejected negotiations on a comprehensive test ban treaty and seemed negative about the proposed testing moratorium.

Carroll said the Soviet reply, while more favorable than that of the United States, "falls short of the firm commitment to end nuclear testing which Admiral LaRoque and I recommended." He added that "the time has come for action, not more encouraging words, if we are ever to slow, stop and reverse the nuclear arms race."

The State Department, in a statement late yesterday, said it is "deeply concerned about the desirability of an uninspected testing moratorium and the verifiability of restraints on nuclear tests."