President Carter has denounced calls for a constitutional amendment to require a balanced federal budget as "political gimmickry" that would be of no help in efforts to reduce the budget deficit.

The president, who earlier had criticized the proposed amendment in generally mild terms, made his stronger views known in a letter to Vern Riffe, speaker of the Ohio House of Representatives. The letter, a response to Riffe's request for Carter's views on the subject, was made public yesterday by the White House.

Release of the letter suggested that after an initially cautious approach, the president is now anxious to take on personally one of his chief Democratic Party rivals, California Gov. Edmund G. (Jerry) Brown Jr., on an issue of Brown's own choosing. Brown, who is expected to challenge Carter next year for the persidential nomination, is an davocate of the balanced-budget amendment and of a constitutional convention to adopt such a law if Congress doesn't act. The president called the convention idea that has been pushed by Brown a "radical and unprecedented action" that "might do serious, irrevocable damage to the Constituion."

Such a convention is not worth the risk of an attempt to rewrite whole sections of the Constitution, Carter said, "particularly when the expressed purpose of the convention would be to consider an amendment as flawed and harmful as one mandating a balanced federal budget."

An amendment that provided "sufficient exemptions" to deal with possible economic and national security emergencies would be so long and complicated that it "would truly be a sham," the president argued. And in that event, he said, crucial budget decisions might be left to "the interpretation of a mathematical formula or economic statistics by a computer analyst or other unidentifiable federal bureaucrat."

"In short," the president said, "any amendment would either be so filled with loopholes as to be meaningless or so rigid as to tie the nation's hands in time of war or depression. I have yet to see proposed constitutional language which does not run one of these dangers. Nor do I expect to see such language because I do not believe it can be written."

Twenty-eight states thus far have enacted measures mandating a constitutional convention to write a balanced-budget amendemtn. The Ohio House has not acted on the issue, according to the National Taxpayers Union, which supports the convention proposal. Approval by 34 states would, under the Constitution, force Congress to call the convention.

The White House has organized a task force, directed by Richard Moe, Vice President Mondale's chief of staff, to combat the convention proposal in state legislatures around the country. White House political aides believe Brown made a serious mistake, which could haunt him next year, in his advocacy of the balanced-budget amendment and the convention proposals. But until now, the president's involvement and rhetoric have been muted.

Carter promised in his 1976 election campaign to balance the federal budget by the end of his term. He long ago abandoned that pledge. In his letter to Riffe, he said he will attempt to eliminate the federal deficit through "prudent, responsible and equitable spending redutions."