Family Dollar CEO Howard Levine said that the board's decision was unanimous and reaffirmed support for its pending merger with Dollar Tree.
But Dollar General CEO Rick Dreiling said the bid was still on the table and antitrust issues wouldn't be a problem.
"We have done extensive antitrust analysis ... the results of which confirm that the transaction [can be] completed," said Dreiling, in a prepared statement. "We remain willing to share this analysis with Family Dollar."
All three of the chains specialize in low-cost consumers goods.
Dollar General calls itself the largest discount retailer in the U.S., with more than 11,000 stores in 40 states.