New York Attorney General Andrew Cuomo on Tuesday said Oppenheimer & Co will restore $31 million to the accounts of customers who were stuck owning auction-rate securities that became illiquid.

The unit of Toronto-based Oppenheimer Holdings Inc is the 14th broker-dealer to agree to buy back the debt in settlements arranged with Cuomo's office. These firms have agreed to more than $60 billion of buybacks.

Auction-rate debt has rates that reset at periodic auctions. Regulators say many brokers marketed the debt as being as safe as cash. Dealers, however, stopped supporting the market in February 2008, causing much of the debt to lose value or become illiquid.

In a statement, Cuomo called the Oppenheimer settlement an important first step in bringing justice to investors who were promised a cash-equivalent investment, while helping to further restore investor confidence.

Oppenheimer was not immediately available for comment.

The settlement was announced a day after Oppenheimer won dismissal of a federal lawsuit in Lexington, Kentucky in which Ashland Inc accused Oppenheimer of fraudulently selling it $194 million of auction-rate debt. U.S. District Judge Jennifer Coffman said the chemical company's claims were not specific enough to let the case move ahead.

Cuomo said Oppenheimer will use a significant amount of available resources to buyback the debt, and has committed to repurchase more when it has greater resources.

All individuals, charities and small businesses with Oppenheimer accounts of less than $1 million are eligible for $25,000 in liquidity, Cuomo said.

Other companies to settle with Cuomo are Bank of America Corp , Citigroup Inc , Credit Suisse Group AG , Deutsche Bank AG , Fidelity Investments, Goldman Sachs Group Inc , JPMorgan Chase & Co , Morgan Stanley , Royal Bank of Canada , TD Ameritrade Holdings Corp , UBS AG , and the former Merrill Lynch & Co and Wachovia Corp .

(Reporting by Jonathan Stempel; editing by Andre Grenon)