By Chelsey Dulaney 

A Delaware court has denied a motion brought by Family Dollar Stores Inc. shareholders to block Tuesday's vote on the company's proposed tie-up with Dollar Tree Inc.--a move intended to push the company to negotiate with rival Dollar General Corp.

Family Dollar shareholders alleged that the company's board breached its fiduciary duty when it declined to consider Dollar General's unsolicited offer for about $80 a share, or $9.1 billion, made in August. Family Dollar's chief executive, Howard Levine, had said there was a "very real and material risk" that Dollar General's offer would fail to pass a lengthy regulatory process.

Meanwhile, the company has pushed forward with its pending $8.5 billion deal to be bought by Dollar Tree. The motion sought to halt Tuesday's shareholder vote on the deal until Family Dollar's board engaged with Dollar General.

The Delaware court declined to grant the injunction on Friday, according to a regulatory filing Monday.

Family Dollar's board had been advised that Dollar General's offer had only a 40% chance of obtaining antitrust approval, and determined that 1,500 stores Dollar General had offered to divest was so far below the level necessary to address antitrust concerns that it wasn't prudent to open negotiations, according to court documents.

Dollar General on Friday said that it was still in discussions with U.S. regulators about its offer, but didn't elaborate on how the discussions had gone.

Earlier this month, Dollar Tree gave an optimistic update on its pending deal, saying it will have to divest a "relatively small" number of stores to secure U.S. antitrust approval of the deal, which could close as early as February.

At the heart of the FTC's review are the similarities among the discount retailers' businesses and how a combination could affect competition and pricing. Dollar General and Family Dollar both sell a variety of consumable and household products at a range of prices, while Dollar Tree primarily sells goods for $1 or less.

Write to Chelsey Dulaney at Chelsey.Dulaney@wsj.com

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