The Justice Department filed suit yesterday against Dorchester County and its county seat, Cambridge, alleging they had violated the Voting Rights Act by discriminating against black voters.

"So much for my powers of persuasion," said Maryland Attorney General Stephen Sachs, who had succeeded in delaying the action one day and who sought to postpone it further while the state audited the Eastern Shore county with the aim of correcting any voting deficiencies.

Sachs pleaded his case with U.S. Assistant Attorney General William Bradford Reynolds yesterday, after which Reynolds filed the two suits in U.S. District Court in Baltimore.

Reynolds, who heads the department's civil rights division, said in a statement released by the department, "While we welcome the very constructive efforts of the state to inquire into the voting rights of its citizens, it is the federal Voting Rights Act that may be violated . . . and therefore the federal government's responsibility to bring enforcement actions of this kind."

John Wilson, a Justice Department spokesman, pointed out that while the state was auditing Dorchester, it was not targeting Cambridge for study.

The Voting Rights Act of 1965 was updated by Congress in 1982 to give the federal courts authority to strike down voting regulations that resulted in political exclusion of minorities. Wilson said this is the Justice Department's sixth suit and the first outside the deep South seeking redress of black voting rights under the amended rules.

The suits maintain that the county and city have denied blacks fair representation by electing officials at large, rather than by district.

As a result, no black has ever been elected to, or nominated for, the County Commission in Dorchester, the suit said. It charged that the at-large system has been "maintained, at least in part, for the purpose of denying blacks an equal role" in elections.

In Cambridge, which has a voting population about one-third black, black City Commission members were elected from majority-black districts until 1972, when at-large voting was implemented, and only one black has been elected since, according to the suit.

The Cambridge suit said the city abandoned single-district voting because of population shifts in the five districts, which would have created black majorities in two of them.

The county suit said voting in Dorchester is racially polarized, and whites generally do not vote for black candidates. Candidates favored by blacks carry predominantly black areas, but nevertheless are defeated in county elections because of the at-large system.

Dorchester County and Cambridge have a long history of racial discord, including a nearly 14-month state of martial law in 1963 after a series of protests there, major fires and riots in 1967 followed by another period of martial law, and the bombing of the courthouse in 1968 when activist H. Rap Brown was to go on trial there.

Sachs said he was disappointed that the Justice Department would not wait for the state to finish its audit of Dorchester, one of 13 counties he is having studied in light of the amended federal voting rights law. He said the state audits will continue in Dorchester and elsewhere.

"We're doing it, Justice Department or no, and we didn't need the Justice Department to tell us to do it," said Sachs.