Dollar General Corp. (DG) on Friday said it is extending its $80-a-share tender offer to buy Family Dollar Stores Inc. (FDO) by two months until Dec. 31, as the offer remained well undersubscribed.

The offer, which had been extended once before, was set to expire at 5 p.m. EST on Friday. As of Thursday, nearly 4.1 million Family Dollar shares had been validly tendered and not withdrawn. Family Dollar has more than 114 million shares outstanding.

Dollar General also said it intends to file a proxy statement with the Securities and Exchange Commission for Family Dollar's special shareholder meeting set for Dec. 11 to vote on the company's deal with Dollar Tree Inc. (DLTR).

Dollar General said it remains committed to buying Family Dollar and that it would mail a proxy statement to its target's shareholders, urging them to vote against the Dollar Tree deal.

Family Dollar has continued to stick with its agreement to be acquired by Dollar Tree for $8.5 billion as Dollar General has pressed ahead with its all-cash offer, which is valued at about $9.1 billion.

As a result, a key Family Dollar investor has voiced growing reservations about the deal with Dollar Tree in light of Dollar General's offer. Elliott Management Corp., which recently owned a 4.9% stake in Family Dollar, said the company's leadership missed an opportunity to let Dollar Tree and Dollar General get into a bidding war.

In turn, the firm nominated seven directors to Family Dollar's 11-member board.

Write to Michael Calia at michael.calia@wsj.com

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