Family Dollar last week rejected a $9 billion buyout offer from Dollar General that it said could run foul of competition law, opting instead for a smaller bid from Dollar Tree.
"The financial benefits of our offer to Family Dollar shareholders are indisputable," Dollar General Chief Executive Rick Dreiling said in a statement on Thursday.
The company's net income rose to $251.3 million, or 83 cents per share, in the second quarter ended Aug. 1, from $245.5 million, or 75 cents per share, a year earlier.
Net sales rose to $4.72 billion from $4.39 billion, helped by higher sales of tobacco products, candy and snacks. Same-store sales rose 2.1 percent.
Analysts had expected the company to report earnings excluding items of 83 cents a share on about $4.67 billion in revenue, according to a consensus estimate from Thomson Reuters.
Dollar General operates more than 11,500 stores in 40 states.
—By Reuters. CNBC contributed to this report.