A prominent Washington law firm that was the first in the city to voluntarily recognize a labor union for support staff also became the first firm hit by a strike yesterday, as its dozen-member staff picketed for higher wages outside the Connecticut Avenue law office.

Bredhoff & Kaiser, which specializes in labor law and represents the AFL-CIO and major international unions, is one of only a handful of law firms in the country with a unionized work force. The firm's 15-member staff of secretaries, paralegals, receptionists and messengers belongs to the Office and Professional Employees International Union (AFL-CIO).

The OPEIU sent letters yesterday to the law firm's leading union clients, asking those unions to "bring whatever influence you can" on the 15-lawyer firm to "help achieve a fair and equitable resolution." Since Bredhoff & Kaiser intends to hire temporary replacements during the strike, the firm's union clients would be "paying for scab labor" if they continue doing business there, OPEIU said.

Law firms have been the target of sporadic unionization efforts in recent years, and while most have strongly resisted union organizers, Bredhoff & Kaiser voluntarily agreed in 1982. Lawyers in the firm have previously described their relationship with the union as usually harmonious.

"The only dispute is money," said Michael Gottesman, a spokesman for the law firm, who said the issue boils down to a difference of roughly $200 a year in company and union wage offers. Bredhoff & Kaiser is offering a $1,000 raise and $700 in bonuses in the first year of a three-year contract, while the union wants $1,900 in salary and bonuses.

The only point of agreement between the union and the firm is that both said the strike was being waged over a small amount of money. OPEIU told the firm's clients that the total cost difference over three years between company and union offers was less than $10,000. "That a strike should occur over this amount of money is an outrage," OPEIU said.

Gottesman, a partner in the firm, said the lawyers believe their final offer is "fair and equitable." The firm's labor costs, including wages, benefits and various payroll taxes, averages $22,407 per employe, not counting customary Christmas bonuses, he said. Under the firm's offer, that figure would rise to $29,182 in the third year of the contract.

But OPEIU overwhelmingly rejected the offer because the union has already agreed to concessions sought by the firm, and because the union contends that Bredhoff & Kaiser can afford to pay raises equal to the $1,800 to $2,000 annual increases offered at other District law firms.

"It really is peanuts," union member and negotiator Lynn Rhinehart said, "But they have never claimed an inability to pay it, and this small amount of money means a lot more to us than it means to them. Our people don't make that much money."

Bredhoff & Kaiser pays a pension benefit in the form of a contribution to a Keough plan and has proposed reducing the contribution from 15 percent to 10 percent of salary, the union said. Current employes would receive a one-time payment of that 5 percent difference, while new employes would not.