Mayor Marion Barry and City Council Chairman Arrington Dixon, both of whom are District of Columbia delegates pledged to support President Carter at the Democratic convention, clashed yesterday over whether delegates should be free to vote for whomever they choose on the first ballot.

Dixon issued a strongly worded press release yesterday blasting Barry for saying Tuesday that he supports an open convention in which delegates are not bound to vote for Carter or Sen. Edward Kennedy on the first ballot, but instead should be able to follow their "political covictions."

Dixon suggested that Barry should resign as a Carter delegate, charging him with trying to "hedge his bets" in case Carter, who has the necessary votes for a first ballot victory if the delegates remain bound, stumbles at the convention.

Hours later, however, Barry issued a written statement in which he disassociated himself from any "dump Carter" movement. "I believe President Carter should, must and will be the Democratic Party nominee," he said.

But in the statement, Barry also repeated his belief that the delegates should not be bound on the first ballot -- a position strongly opposed by Carter's campaign strategists.

Dixon and Barry talked briefly at a delegates meeting last night, and Dixon said later he was satisfied that Barry remains a loyal Carter supporter. However, he said he still disagreed with the mayor on the question of whether the delegates should be released.

Most of the other Carter delegates and supporters at the meeting last night said they also disagreed strongly with Barry's position on the first ballot.

Some, like delegate John Hechinger, said they believed that to free the delegates would disenfranchise citizens who voted in the primaries. Others followed the lead of Democratic State Committee chairman and Carter supporter Robert B. Washington Jr., who said simply, "I support the Carter position."

The delegates voted last night to divide equally funds now being raised to assist members who cannot otherwise afford to attend the convention, which will be held Aug. 11 through 14 in New York.

So far, about $4,000 has been raised, according to City Council member John L. Ray (D-At Large), chairman of the delegation. The delegates had voted previously to apportion the money according to individual need but decided it would be cumbersome to try to determine which delegates were truly needy and which were not. The group eventually hopes to raise $10,000, Ray said.