NEW YORK — Dollar General Corp. has entered the bidding for Family Dollar Stores Inc., making an $8.95 billion offer for the discount store chain that exceeded Dollar Tree Stores Inc.’s $8.5 billion bid.

“For Family Dollar shareholders, our proposal is financially superior to the current transaction agreement with Dollar Tree and would provide Family Dollar shareholders with a substantial premium and immediate liquidity for their shares,” said Dollar General chairman and chief executive officer Rick Dreiling in announcing the bid on August 18.

The offer to buy Family Dollar was made in a letter to its chairman, Howard Levine, and board of directors.

Dollar General said a merger with Family Dollar would generate up to $600 million in savings and profit synergies within the first three years. Dollar General also said that it already has financing in place and its offer does not hinge on obtaining additional financing commitments.

However, on August 21, Family Dollar rejected the acquisition bid from Dollar General, saying that antitrust issues would likely prevent the deal from taking place in its current form. Family Dollar reported that its board voted to back the previously announced merger agreement with Dollar Tree, announced in late July.

"Our board reviewed, with our advisors, all aspects of Dollar General’s proposal and unanimously concluded that it is not reasonably likely to be completed on the terms proposed," Levine said in a statement. "Accordingly, our board rejects Dollar General’s proposal and reaffirms its support for the pending merger with Dollar Tree."

But just hours later on August 21, Dollar General stuck by its proposal and said its bid would clear antitrust hurdles and provides Family Dollar shareholders a better valuation than Dollar Tree’s offer.

"We are disappointed that the Family Dollar board of directors has concluded that our proposal is not reasonably expected to lead to a superior proposal without informing itself of all relevant information," Dreiling said in a statement. "We have done extensive antitrust analysis using experienced advisers, the results of which confirm that the transaction as proposed is capable of being completed. We remain willing to share this analysis with Family Dollar and its counsel and are confident that we will be able to quickly and efficiently resolve any potential antitrust issues."

He added, "We are carefully reviewing and considering our options. Our existing all-cash proposal coupled with manageable antitrust issues continues to make our proposal superior to the current transaction agreement with Dollar Tree."

In a conference call with analysts when Dollar General announced its bid, Dreiling said Family Dollar had in the past rebuffed its advances, none of which had been reported.

Dreiling earlier this year said that he would be stepping down at the end of May 2015, which prompted speculation that Dollar General would not pursue the stumbling Family Dollar after billionaire investor Carl Icahn took a 9.4% stake in Family Dollar and began demanding that the company put itself up for sale. Dreiling now says he would remain on the job of running the combined company though May 2016 and continue as chairman beyond that time.

Dollar General operates over 11,000 stores in about 40 states. Its stores typically measure 7,200 square feet and are often in rural areas not served by national retailers. Dreiling said a marriage with Family Dollar, which operates in more urban neighborhoods, would present an opportunity to learn about doing business in metro areas.

A merger with Family Dollar would create a company with more than 19,000 stores and combined sales of $28 billion. A combination of Dollar Tree and Family Dollar would create a company with 13,000 stores and annual sales of about $18 billion.

At presstime, Dollar Tree hadn’t indicated whether it would raise its bid in response to Dollar General’s offer.