The battle for Family Dollar Stores Inc. escalated on Tuesday, as Dollar General Corp. raised its bid for the second-biggest U.S. dollar-retail chain to $80 a share and took steps to help allay antitrust concerns.

As part of the sweetened all-cash bid, up from a prior offer of $78.50 a share, Dollar General DG, +2.26% increased the number of stores it would be willing to divest itself of to 1,500 if ordered by federal antitrust regulators.