Three weeks after Dollar Tree offered $74.50 a share, or about $8.5 billion for Family Dollar, Dollar General said it would pay $78.50 a share in cash.
"Our proposal is financially superior to the current transaction agreement with Dollar Tree and would provide Family Dollar shareholders with a substantial premium," said Rick Dreiling, Dollar General's chief executive.
News of the bid by Dollar General sent its shares up 9.5% to $62.94 about three hours into Monday's trading session. Family Dollar shares rose 5% to $79.85, indicating Wall Street expects higher bids. Dollar Tree's stock slipped 2.1% to $54.45.
The popularity of dollar stores surged in the recession as struggling Americans looked for alternatives to find cheap groceries and home goods.
But Family Dollar, the No. 2 dollar discounter, has not been performing as well as its two competitors. The company, based in Matthews, N.C., announced in April that it was closing 370 underperforming stores after its profit plummeted more than 30% in the second quarter.
By acquiring Family Dollar, Dollar General, based in Goodlettsville, Tenn., would gain access to urban markets where Family Dollar has most of its locations.
Dollar General, the country's largest dollar store, said if its proposal goes through it would assume $700 million in Family Dollar debt. Dollar General projected the acquisition would generate $550 million to $600 million in cost savings annually.
Combined, Dollar General and Family Dollar, the second-biggest deep discounter, would have about 20,000 stores in 46 states, with sales of more than $28 billion, Dollar General said.
To alleviate potential antitrust issues, Dollar General said it is prepared to unload as many as 700 stores.
"Dollar General has undertaken significant economic and antitrust analysis with respect to the transaction and is confident it can quickly and effectively address any potential antitrust issues," the company said.
If Family Dollar accepts, Dreiling said he would postpone his retirement, slated to begin next May, to oversee the merger through May 2016.