Dollar General Corp. raised its bid for smaller Family Dollar Stores Inc. to $9.1 billion and is willing to divest twice as many locations to ease antitrust concerns after the retailer’s first proposal was rejected for a lower offer.

Dollar General bid $80 a share in cash for Matthews, North Carolina-based Family Dollar, compared with an offer of $78.50 made two weeks ago. The company also said today it would sell as many as 1,500 locations, up from 700 in its previous approach, and pay Family Dollar $500 million if the the deal fails on antitrust grounds.

The sweetened proposal escalates a bidding war against Dollar Tree Inc., whose $8.5 billion offer at $74.50 a share in July Family Dollar has favored. A merger between Dollar General’s two rivals could create a new market leader, intensifying competition while Wal-Mart Stores Inc. is opening smaller-format stores.

“We are confident that our enhanced proposal sufficiently addresses any concerns that led FamilyDollar’s board of directors to reject our prior proposal,” Rick Dreiling, chairman and chief executive officer of Dollar General, said a statement. Dollar General will consider making a hostile bid should it fail to gain Family Dollar’s support, he said.

Family Dollar shares rose 0.6 percent to $80.30 at 8:37 a.m. New York time. The stock had been trading above Dollar General’s rejected offer, a sign that investors expected the chain to raise its bid.Dollar General, based in Goodlettsville, Tennessee, gained 1.3 percent to $64.85 while Dollar Tree was unchanged.

“Family Dollar’s board of directors, in consultation with its legal and financial advisers, will review and consider the revised proposal,” the company said in a statement today.

Randy Guiler, a spokesman for Dollar Tree, declined to comment.

The pursuit of Family Dollar has created tension between it and Dollar General. The companies have publicly traded barbs, accusing each other of misstating facts surrounding a meeting on June 19 to discuss a possible combination.

The battle for Family Dollar began after activist investors Carl Icahn and Nelson Peltz took large stakes in the retailer and then pushed for a sale. Icahn still owns about 3.6 percent of the shares, while Peltz’s Trian Fund Management LP has a 7.3 percent stake.

The deal will generate $550 million to $600 million in annual cost savings three years after its completion, Dollar General said when it made the initial offer.

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