A Democratic group led by the former attorney general Eric H. Holder Jr. has accused the State of Georgia of flouting the Voting Rights Act, claiming that Georgia Republicans reshaped two state legislative districts to minimize the electoral influence of African-American voters.

Mr. Holder’s group, the National Redistricting Foundation, is expected to file suit in Federal District Court in Atlanta on Tuesday. The complaint charges that race was the “predominant factor” in adjusting two districts — the 105th and 111th — in the Atlanta area where white lawmakers had faced spirited challenges from black Democrats.

Both districts were drawn in 2015, through an unusually timed redistricting law that the lawsuit claims violated the Voting Rights Act and the Fourteenth Amendment.

Mr. Holder said Georgia’s district map was a “particularly egregious” case of racial gerrymandering, aimed at restraining the political clout of Atlanta and its suburbs. With the redistricting measure, Mr. Holder said, Republicans had brought about the “silencing of the state’s approximately three million or so African-American residents.”