A House Banking subcommittee yesterday approved a watered-down version of a bill that initially would have subjected branches of foreign banks to essentially the same regulations that govern operations of banks chartered in the United States.

But the subcommitte eliminated provisions that would have prevented foreign banks from setting up branches in more than one state and would have subjected them to monetary policy regulations of the Federal Reserve Board.

The Federal Reserve, the nation's central bank, strongly supported increasing federal regulation of foreign branches. Subcommittee chairman Fernand St. Germain (D-R.I.), who sponsored the legislation, is expected to try to restore the provisions when the bill comes before the full commit.

The bill reported yesterday does require these branches to take federal deposit insurance except in the seven states, such as Maryland, which have state-backed deposit insurance pools.

The bill also make the branches subject to federal bank holding company legislation, which restricts their non-banking activities to a limited range approved by the Federal Reserve Board for U.S. Incorporated bank holding comapanies.

The bill permits these foreign bank branches to keep any non-banking activities they are now engage in except for securities businesses.They must give up any securities activities by 1985.

U.S. banks are not permitted to have branches in more than one state, while foreign banks can set up branches in as many states as they want. Not all states permit foreign branches, howere.

Most foreign branches are concerntrated in New York and California, although there were a rush of branches in Chicago between 1973 and 1975 after the Illinois legislature voted to allow foreign branches to operate in the Loop in 1973.

Foreign branches have assests of about $75 billion in the United States.