The administration formally offered to support legislation yesterday paving the way for subsidiaries of commercial banks to sell mutual fund shares and underwrite municipal revenue bonds and for subsidiaries of savings associations to invest in real estate.

The proposals, presented at a Senate Banking Committee hearing by Treasury Secretary Donald Regan, are symptomatic of another outbreak of administration deregulation fever. If adopted, they will increase competition not only within the banking industry but with nonbank financial institutions such as brokerage houses, insurance companies and retail chains.

"The more the merrier," said Regan, who as chairman of Merrill Lynch and Co. Inc. was credited with inventing the cash-management account, a form of money market fund-cum-checking account that sent shock waves into the banking community.

Yesterday, in his eagerness to promote deregulation, the secretary in one case even went beyond what industry and the Congress had asked by proposing that S&Ls be permitted to establish subsidiaries to buy real estate, provided banks are given the same authority. (S&Ls already have that power, but acquisitions are limited to one or 2 percent of assets, according to the Federal Home Loan Bank Board. Any expansion was deleted from the draft bill because of expected bank opposition.)

Regan reasoned that because thrifts will have "enough new powers to develop for the time being," they should not be authorized to sell mutual funds as well. The idea of giving this power to banks but not thrifts was attacked by Jonathan Lindley, executive vice president of the National Savings & Loan League, which represents the largest S&Ls in the country.

Lindley accused Regan of being inequitable and going against his own free-market policy by trying to dictate which financial institutions could sell money fund shares. Yet, he admitted that not many S&Ls are eager to get into the field.

The administration, Regan testified, supports a federal override of state prohibitions on due-on-sale clauses. This means that federally chartered S&Ls could demand payment of low-interest mortgages when a house is sold, even if there is a state law against it. The Senate bill would give the states several years to rescind the law; the administration would not.

The Financial Institutions Restructuring and Services Act of 1981 is the other side of the coin of the Depository Institutions Deregulatory and Monetary Control Act of 1980. Whereas last year's law freed banks' liabilities by allowing them to pay more interest on savings accounts, this year's legislation seeks to give them the additional asset or lending powers they need to balance their books. In the case of thrift institutions, these powers are considered essential to their very survival.

The 1980 act was many years in the making because of very controversial issues involved. Committee Chairman Jake Garn (R-Utah) yesterday predicted final action on the assets bill by the end of this year. Due to the gravity of the S&Ls'situation, legislators decided to omit from the bill consideration of the thorny issues of interstate branching and revision of the Glass-Steagall Act, which separates commercial from investment banking.