Assets of the nation's money market mutual funds climbed over the $100 billion mark yesterday amid mounting cries from the banking and thrift industries that the government take action to curb them.

Gains of $3.2 billion registered in the past week by the 103 funds pushed their total to $101.2 billion. It was the 10th consecutive weekly increase. At the ends of 1978, money funds totaled $10 billion.

Since the beginning of the year, investors attracted by the funds' high yields, liquidity and check-writing features have increased their assets by more than a third. For the week ended March 4, the average yield was 15.7 percent, far surpassing the 5 1/2 percent passbook rate of savings institutions and topping the six-months certificate rate.

David Silver, president of the Investment Company Institute, the trade organization from mutual funds, called the fund performance " a clear signal from investors that money market funds are what they want -- the highest available yields at minimum risk."

Banks and thrifts hold $400 billion in money market certificates, yet they fear competition by the mutual funds. At separate news conferences yesterday, the U.S. League of Savings Associations and the American Bankers Association called on Congress to curtail money market funds. League President Rollin D. Barnard urged that the funds be required to invest a substantial part of their assests in short-term U.S. Treasury securities as a means of reducing federal borrowing and interest rates.

He also recmmended that the same interest rate ceilings that now apply to money market certificates, issued by banks and thrifts, be extended to money market funds and that reserve requirements be imposed on the funds. These measures would have the effect of lowering the funds' yields and thus their advantage over depository institutions.

"The funds have become an engine of inflation," said Barnard. "At the same time, they have been draining capital from communities across the country and funneling it into the largest money center banks and overseas. That hurts small business, home builders, home buyers, auto dealers and all but the largest financial institutions. They contribute nothing to capital creation."

A substantial number of savings and loans are now operating in the red. The high cost of interest they must pay for funds exceeds the yield on their loan portfolios. Moreover, new deposits have reached a historic low, and in some sectors of the thrift industry there are more funds going out than coming in.

Rep. Jim Leach (R-Iowa) warned recently, "If we alllow the continued spectacular growth of these (money market mutual) funds, in all probability it will drive the death nail into the coffin of the savings and loan institutions."

The Investment Company Institute denies that its members are killing S&Ls. Spokesman Reginald Green pointed out that only 10 percent of the $100 billion in assets is in accounts of $10,000 or less. Were money market fund yields limited, just those small investors would be expected would place their money elsewhere.

The American Bankers Association, which once fought hard against allowing savings and loans to offer checking accounts, also supports the idea of reserve requirements on checking-type accounts offered by money market funds. But, unlike the thrifts, the bankers have adopted an attitude of "if you can't beat'em, join'em."

Their trade organization has asked federal financial regulators to authorize a new deposit instrument that will allow them to compete head to head with the money market funds. This certificate would provide higher yields that currently offered by banks and allow savors to redeem it before maturity without penalty.

Financial regulators will take up the proposal at their next meeting on March 26. Next month Sen. Jake Garn (R-Utah), chairman of the influential Banking Committee, will hold hearings on possible reins on money market funds. Garn has labeled their competition "unfair."