The Securities and Exchange Commission yesterday proposed to regulate the burgeoning stock market business of the nation's banks.

The SEC also proposed to let savings and loan associations operate pooled trust funds without having to register as investment companies.

Both proposals stem from the rapid changes in the financial services industry and the inability of Congress and federal regulators to keep up with the evolving marketplace.

SEC Chairman John S. R. Shad has prodded for faster action, but the SEC decided yesterday only to put out its ideas for comment rather than take any action. The commission said it was moving cautiously because the issues involved are considered very sensitive by other industries and regulators.

Under the plan, banks must register with the SEC if they solicit brokerage business, receive compensation based on stock transactions for accounts, or deal in securities other than municipal securities. That means they must form a brokerage subsidiary, fulfill certain capital requirements and hire employes who have passed the National Association of Securities Dealers examination.

The SEC regulation would not affect institutions, like the Bank of America, that operate a discount brokerage through a subsidiary. It would affect an estimated 500 banks that offer brokerage services directly to customers or under contract with outside firms. The SEC members said they fear investors are not fully protected when dealing with these banks, many of which advertise toll-free telephone numbers in newspapers.

The agency also is responding to protests from the securities industry, which objects to banks being allowed to engage in securities activities without the same restrictions as brokerages must endure.

According to the SEC, the Office of the Comptroller of the Currency, which regulates federally chartered banks, has already expressed a "negative reaction" to its proposal. Neither agency would release the OCC's letter to the SEC. But the comptroller's office did issue a press release this week saying it planned to review the question of supervision of such operations.

Last year, the comptroller ruled that banks can set up brokerage services, but did not specify whether the bank had to form a separate brokerage subsidiary. The Federal Deposit Insurance Corp., which regulates state chartered banks, went even further last year by declaring that these institutions were free to engage in any type of brokerage activities. The FDIC had no comment yesterday on the SEC's proposal.

The savings and loan proposal results from a request by five institutions to establish pooled investments for pension funds without having to submit to SEC regulation.

The SEC sidestepped the sensitive issue of defining what a bank is by asking for public comments on whether it would be appropriate for the SEC to treat S&Ls like banks or whether the matter should be left to Congress.