President Reagan's chief economic adviser said yesterday that financial institutions now hold the key to lower interest rates, and he predicted long-term rates will not move much over "the next few months."

Martin Feldstein, chairman of the President's Council of Economic Advisers, told the Senate Banking Committee that the Federal Reserve Board is helpless to bring interest rates down because the financial community is keeping them up out of fear of renewed inflation.

"What you're saying is that there's little or nothing the Federal Reserve can do to bring down interest rates?" asked Sen. William Proxmire (D-Wis.) .

"That's correct," Feldstein said, adding, "I would anticipate long-term interest rates will not show any substantial movement over the next few months." But, he continued, "If we get recovery well under way six to nine months from now, and Congress takes action to shrink the out-year future deficits, then long-term rates could fall substantially."

Feldstein said the Fed could inject money into the system to lower short-term interest rates, but this action only would fuel inflation fears more and lead to an immediate increase in long-term interest rates.

Feldstein also conditioned his forecast on Congress making it clear soon that it is determined to stem the huge federal deficits looming for the second half of the decade.

Feldstein gave no estimates of how far he expects interest rates to decline at the consumer level. But Housing Secretary Samuel Pierce said earlier that he can envision mortgages dipping to the 9 to 10 percent range.

The FHA rate now is 12 percent, and most conventional mortgages are going for a little over 13 percent.

Pierce said each drop of half a percentage point in interest rates enables 600,000 to 800,000 more potential buyers to qualify for a home.

For the time being, however, the outlook is murky because Feldstein and other forecasters in and out of government indicate more hope than faith about what will happen.

One of the keys is how well the Federal Reserve Board will play under a whole new set of banking rules as it attempts to balance the need to keep enough money moving into the economy to boost recovery without tripping over the line that sparks new inflation.