Simon Property Group, the nation's largest shopping mall owner, stepped up pressure on rival General Growth Properties to accept its $10 billion bid for the real estate company that owns a number of malls across Maryland.

Indianapolis-based Simon made the unsolicited bid for General Growth this month and disclosed it publicly this week, sparking speculation that a bidding war would ensue. The sale would allow Chicago-based General Growth, which filed for bankruptcy in April, to emerge from Chapter 11 bankruptcy protection.

But General Growth rebuffed Simon's offer, saying the company plans to explore alternatives that could include a sale of the company or an effort to raise capital. General Growth CEO Adam Metz wrote in a letter to David Simon, chairman and chief executive of Simon, that the bid was "not sufficient to pre-empt the process" to explore all avenues.

Simon responded with a letter on Wednesday.

"We have tried for many months to explore a transaction with you that would give creditors and shareholders an attractive and expeditious exit from your bankruptcy process and have been repeatedly put off," Simon wrote. "While you pay lip service to time being of the essence, the 'process' outlined in your letter will take many months."

A spokesman for General Growth could not be reached for comment.

Simon said its offer is fully financed and the company is ready to move forward with a transaction. He urged General Growth not to pursue other proposals without "substantively engaging with us."

Simon, which owns Arundel Mills mall, would gain a much larger foothold in Maryland if it acquired General Growth's holdings.

General Growth's properties in the Baltimore area include Harborplace & The Gallery, The Village of Cross Keys, Towson Town Center, White Marsh Mall, Owings Mills Mall, Mondawmin Mall and The Mall in Columbia.