Treasury Secretary Donald Regan took issue yesterday with a new Brookings Institution study that says more than 1,000 savings institutions will merge by 1983 or are in danger of folding.

Testifying before the House Ways and Means Committee, Regan said the Brookings study envisions interest rates in excess of 15 1/2 percent from now through 1983. He said the administration's programs will keep interest rates below that level.

Meanwhile, another financially troubled savings bank was acquired yesterday in the nation's first merger between a savings or thrift institution and a commercial bank.

The Federal Deposit Insurance Corp. said it approved a government-assisted merger of Farmers & Mechanics Savings Bank, of Minneapolis, into Marquette National Bank of Minneapolis, to form a new bank--F&M Marquette National Bank.

The Brookings study, which took a year to complete, predicted that savings institutions' losses over the 1981-83 period will exceed $9 billion and cut the industry's net worth nearly in half.

Given the level of high interest rates and existing government regulations, one in four of the nation's savings and loan associations will cease to exist as independent entities, concluded Andrew S. Carron, a research associate at Brookings.

Regan disagreed, saying the nation's S&Ls will benefit throughout this year as the administration's programs continue to reduce inflation and interest rates.

The secretary also rejected suggestions that the administration should prepare a "standby plan" to aid S&Ls. He said the White House has been monitoring the situation and that it has been working closely with the Federal Home Loan Bank Board to ensure that the industry's problems are being addressed. Bank Board officials had no comment on the Brookings study.

The U.S. League of Savings Associations agreed with Carron that the alternative to the prohibitive cost of a widespread collapse is to help the institutions.

Nevertheless, said U.S. League President William B. O'Connell, "Brookings assumes that the present economic malaise will continue to worsen and that no action will be taken by the administration or the Congress to bring interest rates down and produce a sound economic recovery. We find that impossible to believe."

Data compiled by the National Savings and Loan League indicate that mergers will proliferate if current economic conditions continue into next year. However, there is little reason to believe that there will be wholesale failures, said league president Robert B. O'Brien Jr.

What's more, said O'Brien, "I don't think the current economic scenario will continue. If it does, there will be a lot of nonfinancial institutions failing also."

The National Association of Mutual Savings Banks had no official reaction to the Brookings study.