ATLANTA — A federal judge on Thursday ordered Georgia’s secretary of state to extend the deadline to accept absentee ballots from military service members, their families and citizens living overseas in the event of a primary runoff election on Aug. 21.

U.S. District Judge Steve C. Jones says “it is beyond dispute” that the state will violate election rules under the current system.

The Justice Department sued Georgia last month over the issue, and the case was heard Tuesday in U.S. District Court in Atlanta. Federal prosecutors argued that Georgia’s procedures are “inadequate to ensure that its eligible military and overseas voters can participate fully” in the runoff, should one be necessary.

A call seeking comment from the U.S. attorney’s office was not immediately returned Thursday.

Under Georgia’s election calendar, absentee ballots for the runoff election won’t be sent out until after the Saturday deadline for complying with the federal law, or 45 days in advance of the election.

Secretary of State Brian Kemp has said that he is committed to safe and secure elections for Georgia citizens living here and abroad. A spokesman for Kemp’s office said Thursday evening that the agency had received the order, but did not immediately have a comment on the ruling.

The state has argued that making changes now “would place unnecessary stresses on the elections administrations process,” but the judge said any burden is outweighed by potential injury to overseas voters.

“The potential hardships that Georgia might experience are minor when balanced against the right to vote, a right that is essential to an effective democracy,” Jones wrote in his order.

The order extends the deadline for receipt of absentee ballots by one week to Aug. 31 and orders the secretary of state’s office to send absentee ballots to any eligible overseas voter who requests one by express mail. Those voters would be allowed to return their ballot either by email, fax, or express mail at no cost to them.