PORTLAND — The One Bancorp, struggling to recover from losses rooted in bad real estate loans, announced Monday it was offering bondholders a combination of cash and preferred stock in exchange for $36.8 million in outstanding debt.

Under the offer, which begins Tuesday, holders of the company’s 7 1/2 percent convertible subordinated debentures would receive $100 in cash and three shares of a new series of preferred stock in exchange for each $1,000 worth of principal.

The parent of Maine Savings Bank said its offer is conditional on the valid tender of at least $27.6 million, or 75 percent, of the $36.8 million in outstanding debentures before the Oct. 10 expiration date.

The One Bancorp said the successful completion of the offer is an essential component of the capital recovery plan it announced in January. The bank holding company, with assets of $2.2 billion, recorded six losses in the past seven quarters. It ended the second quarter with a negative net worth of $4.8 million.

“The One Bancorp’s ability to continue as a going concern will depend upon the level of progress it can show in meeting the goals of the capital plan, including the successful completion of this offer, and upon regulators’ willingness to grant the company additional time to complete the plan,” said Vincent E. Furey Jr., president and chief executive officer.

Of the roughly 2,500 beneficial holders of the debentures, most are individuals and many live in Maine, said Tim Welles, vice president of Advest Inc., dealer manager of the offer. The debentures come due in 2011.

The swap would enable the company to increase its capital and reduce the need to service its debt, Welles said.

For the bondholders, he said, it would mean an immediate cash payment equal or larger than the likely liquidation value of the securities as well as a continuing equity interest in the corporation.

Before the offer, the market value of the debentures hovered around $50 per $1,000, Welles said.

The offer provides that each share of preferred stock will have a liquidation value of $10 and be convertible into 26.67 shares of One Bancorp common, which closed Tuesday at 1/4 in over-the-counter trading.

The One Bancorp’s recovery plan seeks to bring the capital of its flagship franchise, Maine Savings, into regulatory compliance. While some elements of the plan have been carried out, the remaining steps include the sale of two subsidiary banks, Bank of Hartford in Connecticut and Southstate Bank for Savings in Massachusetts.