Treasury Secretary Donald T. Regan, in his strongest language to date, blamed banks and other financial institutions yesterday for keeping interest rates high while other sectors of the economy were helping to reduce inflation.

Regan, insisting that the large federal budget deficits were not responsible for the persistent high interest rates, said there doesn't "seem to be a good reason--or should I say there is no good excuse" for those rates to be as high as they are, especially with the recent declines in inflation. He asserted that "real" interest rates--adjusted for inflation--remain "unusually high."

He said that if banks set their charges more in line with the declining inflation rate--which has dropped below 4 percent from about 13 percent at the start of the Reagan administration--interest rates would come down.

"Other major sections of the American economy are now moving in accord with the current environment of low inflation," Regan told a luncheon of the Chemical Manufacturers Association. "And sooner, I hope, rather than later, the banks and other financial institutions must do the same."

However, bankers point out that other factors besides inflation determine the rates they charge, such as bad loans. Besides, some bankers said after Regan's remarks, they don't believe inflation is down to stay.

"There is sort of a latent fear among most investors that while inflation has been reduced substantially, it has also been reduced in the past," said Richard B. Peterson, a senior vice president and economist for Continental Illinois Bank. "In those cases, inflation declined temporarily and began to rise rapidly . . . . We're not sure at all that it's going to stay down."

Regan based his belief that deficits don't push up interest rates on what he called an "exhaustive study" that he said shows there is no definite relationship between the two.

Many economists both in and out of government, however, say that the large spending that produces budget deficits, combined with efforts by the private sector to spend more, leads to inflation. When the Federal Reserve Board, in attempting to keep inflation down, curbs the money supply, that drives interest rates up.

At the same time, economists say, the government's demand for funds to finance its deficit may "crowd out" other big borrowers and drive up interest rates.

"Given the fact that both Congress and the president can't get together on these budget deficits, there's no way that inflation won't rise," Peterson said.

"Well, that is one of those theories that 'everyone knows' that is just not true," Regan said of conventional thought on the relationship of budget deficits and interest rates. "I am not saying deficits are not a serious matter. They cause a lot of problems. It just happens that high interest rates are not one of them."

Yesterday, the federal funds rate--the rate at which banks charge each other for loans, and thus a measure of the cost of money to banks--was 9.5 percent, and the prime rate--the rate banks charge their best customers--was 11 percent, for a "spread" of 1.5 percentage points. Generally banks seek a spread between their cost of money and their lending rate of about 2.5 percentage points, Peterson said. "We think the spread is narrow, now," Peterson said.

Recently, many economists have made conflicting predictions about interest rates, which have declined about one-half a percent in the last two weeks. An interest rate projection by the National Association of Manufacturers released yesterday predicted that the prime rate could rise to 12 percent by the end of the year, while other private and government economists have said the recent slowing of economic growth, moderate increases in the money supply, and reductions in inflation should help interest rates edge downward slightly this year and in 1984.

Regan, former chairman of Merrill Lynch & Co., also criticized Congress, which returns next week from its August recess, for failing to cut spending. He reiterated the administration's policy against tax increases.

In addition, Regan, a past critic of Fed policy, said the administration has been "strongly urging the Fed to do everything in its power" to stay within its target range for growth of the money supply. "At the moment they are," Regan said.