A coalition of unions representing the District's 32,000 employes repeated its demand yesterday for a 9.1 percent pay increase this year, stating for the first time publicly that the unions would be willing to strike if Mayor Marion Barry holds firm in his refusal to negotiate.

Strikes by city workers are illegal under the city's new civil service law. But union spokesman Robert E. Petersen, president of the Greater Washington Central Labor Council (AFL-CIO), said that same law also requires the mayor to bargain collectively with city workers over wages.

"The fact that the mayor has refused to bargain collectively is a violation of the law," Petersen said, speaking for the newly formed Public Employees Union Coalition. "The mayor broke the law first. We didn't start it."

The possibility of a strike, or some other job action, has always been the unspoken factor in this ongoing dispute between Barry and the city's labor force, ever since the mayor unilaterallydecided to give city workers a 5 percent pay increase while federal workers have been granted a 9.1 percent pay raise.

Barry officially transmitted his request for the 5 percent increase to the City Council on Tuesday and, in a press conference, rejected once again the unions' demand for collective bargaining. Barry also dismissed as "a good labor ploy" the unions' petition to the Public Employee Relation Board (PERB), asking the board to certify all city workers collectively as one unit for the purposes of bargaining for the fiscal year that began yesterday.

"We reject the argument that anything above 5 percent would lead to massive layoffs of government workers," Petersen said. "We do not think that the employes of this city should be placed on the horns of a dilemma which was not of their own doing."

Petersen said that union attorneys have begun preparing for court action, which would be carried out simultaneously with any strike. Petersen said that if the PERB does certify the city workers coalition for bargaining in a decision due next week, then the unions would take Barry to court to force him to negotiate the wage issue.

Even if the city workers are not certified as a single unit, Petersen said the issue might still end up in the courts, because the unions would challenge the mayor's authority to unilaterally set pay increases.

The labor press conference, attended by the heads of most of the unions in the coalition, began on the fifth floor of the District Building at the same Barry was unveiling to reporters his budget for fiscal year 1982. That budget includes no increase at all for city workers, and the mayor said that any pay raise next year would depend on Congress granting the city additional funds.

Petersen called the mayor's 1982 budget proposal "preposterous" and "totally irresponsible. I can't imagine someone doing something as foolish as what the mayor has done" by not including any pay raise for 1982, Petersen said.