(Reuters) - Dollar General Corp (>> Dollar General Corp.) raised its bid for Family Dollar Stores Inc (>> Family Dollar Stores, Inc.) to $9.1 billion, and warned it may turn hostile and appeal directly to shareholders if the new offer was rejected.

The No.1 U.S. deep-discount retailer also said it would pay a break-up fee of $500 million if the deal ran foul of competition law, seeking to overcome Family Dollar's stated reason to reject its earlier $8.95 billion cash offer.

Family Dollar stuck instead with an $8.5 billion cash-and-stock bid from Dollar Tree Inc (>> Dollar Tree, Inc.) made in late July.

Family Dollar said on Tuesday its board would review Dollar General's new offer and that it was committed to the Dollar Tree deal.

Any deal will net Family Dollar CEO Howard Levine between $690 million and $750 million, based on his 8.2 percent stake in the company.

Analysts said shareholders could pressurize the company to accept Dollar General's offer.

"Family Dollar's board will be hard pressed to justify rejecting Dollar General's revised offer without risking a massive backlash from its shareholders," BB&T Capital Markets analyst Anthony Chukumba wrote in a note.

Family Dollar's shares rose more than 1 percent to an all-time high of $80.97 on Tuesday, slightly above Dollar General's offer of $80 per share, suggesting some investors held hopes of higher offers.

The fight for Family Dollar comes at a times when dollar chains are struggling with minimal or no gross margin growth as they try to keep lower-income shoppers from being lured by Wal-Mart Stores Inc (>> Wal-Mart Stores, Inc.) and Target Corp (>> Target Corporation).

Wal-Mart is doubling down on small-format stores, typically one quarter the size of its supercenters, a move that could result in increased competition for the dollar stores.

Research firm Wolfe Research said in a note that the best outcome for all parties was for Dollar General to merge with Family Dollar as the combination would be the best placed to compete with Wal-Mart.

"A levered Dollar Tree/Family Dollar with a standalone Dollar General is likely to embolden Wal-Mart to further accelerate its small-box plans, leading to additional market share gains and diminished consumer choice," Wolfe Research analysts said.

CLOSING MORE STORES

Dollar General also said it was willing to sell up to 1,500 stores to clear the antitrust review, up from the 700 it had proposed earlier.

The company said it hired Richard Feinstein, a former director of the Bureau of Competition at the Federal Trade Commission (FTC), to further "validate its antitrust analysis".

Playing down antitrust concerns, Dollar General said its documents would show that the products it offered were not unique as they were also available at most mass retailers, drug and grocery stores.

It also said that Wal-Mart, and not Family Dollar, was the primary driver for the company's pricing decisions.

A transaction with Dollar General faces little risk of being stopped by the FTC in the absence of documents that show both companies only watch each others' pricing practices, said Jonathan Lewis, an antitrust expert with law firm Baker Hostetler.

Dollar General and Family Dollar offer goods at multiple price points, while Dollar Tree sticks to a $1 or less format.

Dollar General's shares were up 0.5 percent at $64.36.

DOLLAR TREE FRIENDLIER?

The Dollar Tree bid is friendlier to Family Dollar's management.

Levine, son of the founder of Family Dollar, would remain CEO of Family Dollar if it was bought by Dollar Tree.

If Dollar General succeeds in buying Family Dollar, Levine is widely expected to lose his job, although this has not been confirmed.

However, Levine stands to make about $745 million from his stake of 9.3 million shares in Family Dollar, which makes him the largest shareholder as of late July.

Dollar Tree's cash-and-stock offer of $74.50 per share proposal would bring him about $50 million less.

He would also be eligible to receive annual salary of at least $1.2 million and stock options for his continued role as CEO of the unit.

Nelson Peltz's Trian Fund Management LP, the second-biggest shareholder in Family Dollar after Levine, declined to comment on the new offer. It had earlier endorsed Family Dollar's rejection of Dollar General's bid.

(Additional reporting by Abhirup Roy, Olivia Oran and Diane Bartz; Editing by Saumyadeb Chakrabarty)

By Sruthi Ramakrishnan