NEW YORK – New York Attorney General Andrew Cuomo said regulators have reached settlements with Merrill Lynch & Co., Goldman Sachs Group Inc. and Deutsche Bank over their roles in selling risky auction-rate securities to investors.

Under the agreement, Cuomo said, Merrill Lynch will buy back roughly $10 billion to $12 billion of the investments from investors by Jan. 2 and pay a fine of $125 million.

Deutsche Bank, which must buy back about $1 billion of auction-rate securities, has been fined $15 million. Goldman Sachs has $22.5 billion of the securities to buy back, and was fined $1.5 billion.

“This has been a great day of progress,” Cuomo said during a conference call.

Cuomo and other regulators previously reached $42 billion worth of settlements with five major Wall Street banks, including Citigroup Inc. and Switzerland's UBS AG. The attorney general threatened earlier Thursday to sue Merrill Lynch if an agreement was not reached by the end of the day.

The investigations are examining how brokerages sold auction-rate securities before the $330 billion market collapsed in February. Federal and state authorities believe that banks pitched the investments as safe.

Merrill Lynch earlier this month agreed to buy back an estimated $12 billion in auction-rate securities, though the company said it has already been buying back the debt. Merrill Lynch's plan was voluntary and put no set timetable on the transactions.

Cuomo said earlier Thursday he wanted the investment bank to buy back the securities within a set period of time, and to also pay fines for having pitched them as safe investments to customers.

Also Thursday, Massachusetts Secretary of State William Galvin said Thursday Merrill Lynch agreed to settle a similar dispute.

Galvin, who is the top securities regulator in Massachusetts, said the agreement calls for Merrill to buy back beginning Oct. 15 all illiquid auction rate securities from investors who have less than $3 million on deposit.

In addition, after Jan. 15, Galvin said Merrill agreed to buy back auction-rate securities from investors with deposits on account of $100 million or less. Massachusetts filed its enforcement action on July 31.

Merrill declined comment on the Massachusetts case.

The auction-rate securities market involved investors buying and selling instruments that resembled corporate debt, but the interest rates on the investments were reset at regular auctions, some as frequently as once a week. A number of companies and retail clients invested in the securities because they could treat their holdings almost like cash.

But the market for them collapsed in February amid the downturn in the broader credit markets. Regulators have been investigating the collapse in the market to determine who was responsible for its demise and whether banks knowingly misrepresented the safety of the securities when selling them to investors.