Sen. Jake Garn (R-Utah), chairman of the Senate Banking Committee, said yesterday he still intends to put his controversial banking bill to a vote before the Aug. 19 recess.

However, despite an offer by Garn to negotiate the sensitive issue of additional securities power for banks, the securities industry remains adamantly opposed to his bill.

Garn postponed a mark-up session scheduled for last Wednesday when it became apparent a rival measure had the support of a majority of the 16 members. But he said yesterday he will bring his bill before the committee by next Thursday at the latest.

Garn's bill would allow affiliates of banks to underwrite and deal in municipal revenue bonds and to organize and operate mutual funds. Savings institutions would also be allowed to sell mutual funds. However banks would not be required to transfer existing securities activities to the new subsidiaries, an arrangement that could give banks a competitive advantage over brokerage firms. A substitute bill omitting these additional securities powers was introduced by Sen. John Heinz (R-Pa.).

Leaders of the Securities Industry Association met yesterday with Heinz and then later with Garn and Treasury Secretary Donald Regan. The Reagan administration has urged the securities provision be included. SIA president Ed O'Brien said nothing was resolved in the second meeting. He said the SIA feels there is not enough time this session to overhaul the securities industry. So the industry is "100 percent behind the Heinz bill."

Spokesmen for the banks and savings and loans trade groups indicated they would continue to support the Garn bill as a vehicle for amendments. But the National Savings and Loan League added it would "welcome the Heinz bill if that's what the committee decides to do. . . . "