NEW YORK (TheStreet) -- Dollar General (DG) isn't walking away from its $78.50-a-share cash offer for Family Dollar (FDO) , even after the company's bid was rejected earlier in August on antitrust grounds. Family Dollar continues to favor a lower-priced merger offer from competitor Dollar Tree (DLTR) , which Family Dollar said  carries lower regulatory risks and was negotiated after a thorough six-month sale process.

Even so, Dollar General said on Thursday it isn't backing down from its offer.

"[We] remain firmly committed to the acquisition," Dollar General said of its proposed merger with Family Dollar. Dollar General believes that in addition to offering a higher price, its proposed merger simply makes more sense financially. Antitrust hurdles, the stumbling point in Dollar General's bid for Family Dollar, are manageable, the company said.

Read More: Trian Management Key in Family Dollar and Dollar General Battle

"The financial benefits of our offer to Family Dollar shareholders are indisputable, and the proposed combination would unlock tremendous value for Dollar General shareholders," Dollar General said in a Thursday press release appended to earnings.

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"We continue to believe the potential antitrust issues are manageable and that our transaction as proposed is both superior and achievable," the company concluded.

Dollar General on Thursday reported slightly disappointing second-quarter earnings, and missed analysts' estimates on sales. Second-quarter sales at the discount retailer rose 7.5% to $4.72 billion, slightly below estimates of $4.77 billion. Earnings per share were 83 cents, meeting forecasts.

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