Mayor Sharon Pratt Dixon's office said yesterday it will try to settle a legal dispute between the District government and about 60 blind vendors who claim the city owes them $620,526.

Spokesmen for the vendors' group said they were pleased with Dixon's response to a letter and petition they presented to her office yesterday, asking her to intervene in a fight that had dragged on for years between the vendors and the administration of Dixon's predecessor, Marion Barry.

"I'm buoyed by the decision," said Robert Humphreys, attorney for the vendors. "This demonstrates to me a quick understanding, and a very sympathetic attitude toward the vendors."

The vendors want the mayor to honor a ruling last April by U.S. District Judge Oliver Gasch ordering the city to pay them the money. Gasch found that the District had mismanaged a program for blind vendors who run snack shops and newsstands in federal and city buildings.

The vendors pay a percentage of their net profits to the city to manage a program training blind vendors to run small businesses. The judge ruled that the vendors had paid for services they never received, and must be paid back.

The city appealed the ruling and has not paid the money.

Humphreys said the vendors' group repeatedly had offered to settle the case out of court, but was rebuffed by the Barry administration. A group of 16 vendors gathered outside the District Building yesterday in hopes that Dixon would respond more sympathetically.

"I trust her being new, with the higher goals she's set," said Bettye Arrington, 38, of Temple Hills, who sells snacks in the Waterside Mall in Southwest Washington.

The vendors who were gathered outside the District Building heard what they had hoped to hear.

The Barry administration's handling of the program "was unfair to you," Virgil Thompson, Dixon's director of constituent services, told the group. "Hopefully, you'll be reimbursed and the District will be reimbursed for what appeared to be illegal transactions."

A federal law gives blind vendors preference in operating snack bars and vending machines in federally owned or leased buildings. The law also authorizes the states and the District to appoint nonprofit agencies to oversee the programs.

Until 1984, the local program was run by a nonprofit group. Late that year, the contract was awarded to a for-profit food services company.

The vendors argued that the for-profit company should have been prohibited from managing the program. The company said the city could be seen as a nonprofit group that gave the program to a subcontractor.

The vendors "have a very good case," Thompson said.