"An unnecessary and unjustified rise in interest rates" could jeopardize the economic recovery, Treasury Secretary G. William Miller told reporters in Chicago today.

But he added that he does not think this will happen because the recent fuss over rising interest rates has prompted both the chairman of the Federal Reserve Board and some private bankers to concede that interest rates probably are too high.

Miller repeated recent administration criticism of both the private banks and the Fed for the early sharp increase in rates. "We should not shoot ourselves in the foot because of weekly wiggles in some esoteric figures" for the money supply, Miller said, referring to the Fed's credit tightening response to rapid rises in the weekly money supply figures last month.

He did not say that the Fed should abandon its year-old method of controlling the money supply through monitoring directly the growth of bank reserves. But he said that the board should have some limit on how high it is prepared to let interest rates rise.

It showed in the spring that it had an effective limit on the down side, he remarked. The Fed then let the money supply stay well below the target ranges, as it did not want rates to fall too far. There ought to be a point where the Fed "temporarily would allow growth to go beyond its targets to keep interest rates down," Miller said.

He would not say what the correct rate for the prime should be, but said that it should be "lower than now." For the auto and housing industries to recover properly, businessmen should be assured that interest rates will drop over the next six months, he said.

The Treasury secretary was cautious about the prospects for inflation over the coming months. He said that it would be a "false promise" to tell Americans that there is a quick cure for inflation.

But he claimed that a continuation of the administration's "responsible fiscal monetary and credit policies" can lead to "genuine, if gradual, progress in our efforts to reduce the underlying inflation rate."

In his address to the opening session of the American Bankers Association here this morning, Miller defended President Carter's record, and the new economic program put forward by Carter on Aug. 28. But he told the bankers that the nation is facing serious challenges, with inflation and poor productivity the foremost domestic problems.

He told a press conference that America's dependence on foreign oil means that inflation can come down only slowly and can be affected dramatically by changes in oil prices.

He called Carter's anti-inflation policies "enormously successful," but said that they could not be measured "in terms of results." The onerous rises in cost over Carter's years in office were beyond the control of the administration, he said.

Miller emphasized the Carter administration's success in "hammering out" a national energy policy and cutting by 25 percent from its 1977 level the amount of oil imported into America.

He also said that firm control of federal spending has helped the nation to resist inflation during Carter's term as president. The administration has kept federal spending on nondefense items down so that the federal budget has grown on average by less than the economy as a whole, the Treasury secretary told reporters.

"The recession of 1980 may prove to have been one of the shortest on record," Miller said to the assembled bankers. The evidence shows that the administration was correct in refusing to stimulate the economy earlier this year.

Miller went on to say that "while we must, of course, take steps to reinforce recovery from this year's downturn, top priority must be assigned to initiating and implementing policies that will cure outstanding economic ills, both at home and abroad."

The need to recycle huge sums of money from oil-rich countries to those with balance-of-payments deficits is of great concern to many of the bankers here.