Mayor Marion Barry's trip to Las Vegas to see the Sept. 16 championship fight between Sugar Ray Leonard and Thomas (Hit Man) Hearns was paid for out of public funds, city officials said yesterday.

The mayor's air fare and some of his expenses were paid for the by the D.C. Armory Board, operator of the Armory and RFK Stadium, in hopes that the mayor would have an opportunity to use his influence to convince bigtime boxing promotors to schedule fights here, officials said.

Barry, who paid for his own fight ticket, agreed to submit a report to the board describing his labors and their fruits, but has not yet done so, Armory officials said.

"The board voted that he Barry would go out there and make contacts with the Don Kings, the Bob Arums, those individuals involved in boxing," said Armory general manager Robert Sigholtz. Don King and Bob Arum are two of boxing's most prominent promoters.

"The idea was that the mayor, with his prestige, would get in to see people" who might have ignored another emissary, said Armory board member and Barry appointee Stuart J. Long.

Sigholtz said the board, a city agency which supports itself from revenues generated primarily by the rental of RFK Stadium to the Redskins, paid for Barry's transportation to and from Las Vegas. Though he was uncertain how much the air fare was, he said that he was certain the mayor did not fly "first class." Airlines spokesmen said that a round-trip economy flight between Washington and Las Vegas costs $758.

In addition, the board paid Barry a per diem of about $45 a day while he was in Las Vegas, according to Long, a former Barry campaign fund-raiser.

Long said the board decided several weeks before the fight to send Barry to try to boost local boxing. However, both he and Sigholtz said yesterday that they could not remember who first came up with the idea of sending the mayor.

"I know he did get to talk to some people," said Long, who also attended the fight but on his own money. Edward Meyers, Barry's press spokesman, said Barry spoke with promoter King while he was in Las Vegas, but did not know whom else the mayor was able to reach. Neither King nor Arum could be reached for comment yesterday.

Shortly before the fight, Barry told a reporter that he was going to attend the fight at the request of Mrs. Leonard who wanted her husband to have as much support as possible.

Long said the board tries to send a representative -- it is often Sigholtz -- to major boxing matches and other sporting events around the country when it appears that there is the opportunity to lobby sports moguls with the pull to arrange sports events in the District.

He said he believed, for example, that such lobbying efforts helped obtain for the city the latest incarnation of the Diplomats soccer team (now defunct), and a favorable arrangement for the closed-circuit telecast of the Leonard-Hearns fight at the Armory.

Long said that Barry was particularly interested in lobbying for some future Sugar Ray Leonard fight which would perhaps be staged in the 55,000-seat RFK stadium. The Armory, much smaller at about 10,000 seats, is a less likely site for such a fight.

The mayor paid for his own fight tickets, which ranged from $100 to $500, and also supplemented the per diem to pay his hotel and other expenses, Long said.

The District has had little in the way of big-time boxing in recent years. The last bout of note was a contest between professional football player Ed (Too Tall) Jones and Fernando Montes of Mexico at the Armory in November 1979. Jones won but returned to football soon after.

There was also supposed to be a World Boxing Association lightweight championship fight at the Armory that night, but promoter James L. Denson was unable to come up with an advance payment of $60,000 demanded by champion Ernesto Espana, who then refused to fight.