The hedge fund run by Sears CEO Edward Lampert issued its strongest warning to date that the retailer must “immediately” take steps to right itself, calling on the company to restructure debt and sell off assets.

Lampert’s ESL Investments wants Hoffman Estates-based Sears Holdings Corp. to restructure more than $1 billion in debt and sell about $1.5 billion in real estate and about $1.75 billion other assets, including the company’s popular Kenmore appliance brand, according to a proposal made public in a regulatory filing Monday.

ESL offered to buy Kenmore and certain other divisions of the retailer’s business in April. But the latest proposal is broader and pushes the company to act more quickly in the face of “significant near-term liquidity constraints,” including a $134 million debt payment due next month.

Sears said it had received ESL’s proposal and directed the company’s management and advisers to work with the hedge fund. A board committee already negotiating with ESL on the proposal to buy Kenmore will review the proposed real estate deal, Sears said.

Sears has lost more than $11 billion since 2011 and has struggled to win back shoppers. The company closed hundreds of Sears and Kmart stores and sold pieces of its business, including the Craftsman tools brand. It also sold more than 200 stores to real estate investment trust Seritage Growth Properties, in which Lampert holds a stake and serves as chairman of the board.

Sears, Roebuck & Co. was founded in the 1880s by Richard Warren Sears and Alvah Curtis Roebuck as a mail-order company selling watches. Sears was king of the U.S. shopping landscape for decades. Its catalog featured items from bicycles to sewing machines to houses. The company began opening stores in 1925.