Federal Reserve Board Chairman Paul Volcker called yesterday for more spending cuts to shrink the budget deficit, which he said was a major factor in the continuing high cost of borrowing money.

It was Volcker's first public statement since President Reagan revealed last week that the administration might have to cut spending more deeply than it had expected in order to keep to its targets for the federal deficit.

Administration officials are deeply concerned about the continued record level of interest rates, and the failure of the bond market to rally in response to Reagan's economic program. Budget Director David Stockman is reportedly seeking deeper spending cuts for 1983 and 1984, perhaps including cutbacks in planned defense spending.

However, Reagan reaffirmed this week his commitment to the defense build-up, which many analysts believe is not compatible with balancing the budget by 1984. The president also said he would keep next year's deficit to the $42.5 billion forecast, and would balance the 1984 budget.

Volcker held out hope yesterday of easier credit markets between now and the end of the year, although he refused to back off from the tight money policy that has helped to drive interest rates up this year. As one key measure of money supply has been growing below its target range so far this year, "growth during the remainder of the year should be somewhat larger than it was up until now," the Federal Reserve Chairman said on PBS's MacNeil-Lehrer Report news show.

However he would not predict when interest rates would come down, and said that the Fed's policy of "restraining the growth of money and credit" was "absolutely fundamental to dealing with the inflation problem." Volcker also pointed out that many sectors of the economy have not really been hurt yet by high interest rates, although the housing and auto industry are particularly vulnerable to high rates.

The next big move in rates would probably be downward, Volcker said, as inflation was coming down more rapidly than predicted and the economy was slowing.

However, Volcker said that there are "very heavy credit demands continuing in the economy, not least of course from the U.S. government" and that "a lot more remains to be done to get that budget in shape." The size of the deficit was crucial for the financial markets, and interest rates he said.

The president admitted when signing the tax and budget bills last week that the administration may need to make bigger spending cuts than it first estimated to meet its forecasts of a shrinking deficit. High interest rates, as well as being partly a result of the large federal deficit, also swell federal spending and thus worsen the deficit.

The administration assumed a sharp fall in interest rates when drawing up its budget numbers. This has not yet materialized, and so the cost of servicing the government debt this year and next will probably be significantly higher than allowed for in the July spending review. This is one reason why many market analysts expect next year's deficit to be close to this year's predicted $55 billion.

Interest rates on government debt yesterday soared to new record levels, underscoring the importance for the administration of bringing interest rates down.

Meanwhile, Charles Schultze, the chairman of former president Carter's Council of Economic Advisers, told reporters yesterday that he expected interest rates to stay relatively high even if inflation comes down somewhat. Money policy is so tight, and the tax bill was so large, that rates are bound to be high, Schultze said. He added that he did not think it would be of great benefit to the economy if the Fed eased up.

The economy was likely to be "neither a disaster nor utopia" under Reagan, Shultze said. He expected "a very long period of the same thing" as now -- a sluggish economy with little productivity growth and some easing of inflation.

Further cuts in nondefense spending would be a bad thing for the United States, Schultze said, although without them there would be even more upward pressure on interest rates.