Activist investor Elliott Management sent a letter to Family Dollar's board, nominating seven new directors on Friday. The move sent the retailer's shares about 1 percent higher in after-hours trading.
In a letter to Family Dollar CEO Levine, Elliott said Dollar General's offer was "clearly superior'' to Dollar Tree's bid. "This opportunity appears to have been missed, and the company must now seek to maximize value for shareholders...," the investor said.
Family Dollar confirmed that it received the letter and said it would review it "in due course."
The hedge fund said it wanted to "protect our interests as one of Family Dollar's largest shareholders" and ensure that its board does everything within its power to provide Dollar General with an even playing field in its continuing efforts to acquire the Family Dollar.
Last month, Family Dollar spurned Dollar General's $9.1 billion all-cash bid earlier, saying the offer still not address its antitrust concerns. Family Dollar instead said it was sticking with a lower $8.5 billion cash-and-stock offer from Dollar Tree.
After being rejected twice, Dollar General took its bid hostile and approached Family Dollar shareholders directly.
The activist manager said it has a beneficial and economic ownership interest of about 4.9 percent of all Family Dollar's outstanding shares.
—Reuters contributed to this report.