Senate Banking Committee Chairman Jake Garn (R-Utah) yesterday opened two days of congressional hearings into money market mutual funds with a statement about the unfair competition between the funds and thrift institutions. The statement was made amid indications that Garn has softened his position on the need for legislative curbs.

Garn, who in the past has strongly urged restraints on the funds, said the best remedy to end the competitive unfairness was long-term action to deregulate other competitors. But he was silent on any possible short-term remedy, which has become the subject of great controversy.

Garn's comments tended to defuse the hearings, which had threatened to become explosive because of the volume of "save our funds" letters sent to Congress in response to threats to reduce their yields.

An aide to Garn said yesterday the senator's position on money market funds has softened somewhat as he questions whether putting reserve requirements on transaction accounts would have much impact on yields or on driving money back to the thrifts.Thus the primary issue for hime becomes that of fairness. The aide added that Garn now takes a neutral stand and is not now preparing any legislation. Also, the Reagan administration has come out against further regulation of the funds.

Committee member Sen. John Chafee (R-R.I.) was more emphatic. "I am opposed to seeking regulation for the sole purpose of making the competition less attractive," he said. "I am even more strongly opposed to such an approach when the small savers of this country would bear the brunt of it."

Securities and Exchanges commissioner John Shad and member John Evans testified against putting reserve requirements on money market fund transaction accounts as unnecessary to protect investors. As for helping thrifts, the pair said they preferred subsidies through government purchase of their low-yield loans rather than reducing rates for savers. They also urged revision of the 50-year-old Glass Steagall Act that prevents banks from engaging in securities activities.

In addition to reserve, the question of redistribution of assets arises in connection with money market funds. Capital tends to gravitate toward the largest banks in the country at the expense of smaller banks and thrifts. Sen. Paul Sarbanes (D-Md.) asked the SEC to prepare a confidential breakdown of how much fund money is going into which banks.

At today's session the thrifts, small banks and housing industry will testify in support of restraints on money market funds. The only major government agency that has yet to take a stand is the Federal Reserve. A spokesman said yesterday its policy paper would be ready in the "immediate future." Chairman Paul Volcker was trying to arrange a date to testify later this month or next.