The Justice Department announced on Thursday that it had filed a motion to join a lawsuit against the New York City Board of Elections, alleging that the board’s Brooklyn office violated federal voter registration law by erasing more than 117,000 Brooklyn voters from the rolls before the primary election simply because they had not voted in previous elections.

The filing accused the board of failing to take several steps that are normally required before a voter’s name is removed, and also raised concerns about how the board oversaw the Brooklyn office’s handling of the voter rolls.

The petition by the Justice Department to intervene in a lawsuit filed in November by Common Cause New York, a good-government organization, lends significant muscle to an effort to hold the agency responsible for a chaotic Primary Day in April, when many voters in Brooklyn were surprised and infuriated to learn that their voter registrations had been canceled.

With the filing on Thursday, the Justice Department becomes perhaps the most potent of the government players trying to force changes at the board. The city comptroller, Scott M. Stringer, and the state attorney general, Eric T. Schneiderman, both opened inquiries into the board’s procedures after its bungled Primary Day performance, and Mayor Bill de Blasio has called for spending $20 million to improve city voting procedures.