The House of Representatives is expected to pass a resolution next week pledging the full faith and credit of the government behind the $100,000 federal insurance on funds deposited in U.S. banks and savings institutions. The Senate probably will follow suit.

Moreover, administration sources said yesterday it was likely that President Reagan or Treasury Secretary Donald Regan would make a similar public statement within the next 10 days.

The House resolution, which will be introduced Monday at the request of the thrift industry and its regulators, seeks to reassure Americans, worried by reports of the industry's financial difficulties, that their money is safe.

"Persons with deposits of $100,000 or less are totally safe, and there is no way anyone will lose a dime," declared Rep. Fernand St Germain (D-R.I.), chairman of the Banking Committee.

He said the resolution was necessitated by "numerous reports and news stories that have discussed serious problems in the thrift industry, raising false fears that depositors would face problems if there were large-scale failures of institutions."

A story last month in a local newspaper about the operating losses and possible merger of a small Connecticut savings and loan allegedly caused customers to withdraw $3 million in deposits in three days. There have been articles questioning whether the resources of the government insurance agencies, particularly the Federal Savings and Loan Insurance Corp., would be adequate if substantial numbers of S&Ls should fail or be merged. Legal questions have been raised as to whether a guarantee from a federal agency is as good as one from the U.S. Treasury.

Last year savings and loans suffered a $25 billion net outflow of deposits. The thrift industry has complained for several years about uninsured money market mutual funds, which it claims are siphoning money from savings accounts as people are attracted by higher rates.

How much of the drain can be attributed to competition and how much to lack of confidence is difficult to measure. The Brookings Institution recently reported that one-third of the savings withdrawn from thrift institutions went into commercial bank accounts with identical interest rates.

The idea of addressing the issue publicly in hopes of dispelling any notion of danger to insured savings appears to have evolved last month. The President's Commission on Housing recommended that "the federal government should make clear and explicit its responsibility to maintain the viability of the financial system, including a commitment to use whatever resources are necessary to achieve that goal."

Federal Home Loan Bank Board Chairman Richard Pratt urged last month and again this week that Congress or the administration provide reassurance. The U.S. League of Savings Associations wrote the president last Tuesday requesting a public statement.

Should Reagan do so, it apparently would be the first time since the Depression that a president has had to reassure Americans publicly that the banking system is safe. Forty-nine years ago yesterday, President Franklin Delano Roosevelt devoted his first fireside chat to explaining the banking system in nontechnical language, "so that the great mass of our citizens . . . would be relieved of their anxiety as to whether they would ever see their money again."

Of course, the situation was entirely different then; the nation's banks were shut after some had failed, and there was no government insurance. But the message is the same: "You people must have faith," FDR said. "You must not be stampeded by rumors or guesses. Let us unite in banishing fear. We have provided the machinery to restore our financial system; it is up to you to support and make it work."