Bert Lance, director of the Office of Management and Budget, sharply criticized the nation's commercial banks yesterday, for "unjustified" increases in the prime interest rate - increases he said might cause serious inflation.

The prime rate is the interest banks charge their biggest and best customers. It recently has been increased from 6.25 per cent to 6.75 per cent in two steps.

At the same time, Lance laid the blame for the higher prime rate at the door of the Federal Reserve Board, which has tightened up the money supply for fear that a liberal monetary policy followed earlier this year would be inflationary.

Lance's cautious but critical comment about the effect of the Fed action, especially as it might affect long-term interest rates such as mortgage costs, was as close as the Carter administration has come to an open controversy with the Fed and its chairman, Arther F. Burns, over monetary policy.

The budget director's critique of the way banks have raised the price of their loans was also a clear example of "jawboning," a practice the administration has shuned in the industrial area as an interference withthe private decision-making process.

Lance said he was worried about the effect of high interest rates in consumer purchases and confidence. He also blamed the recent slide in the stock market in part on "uncertainty" generated by high interest rates.

Lance said yesterday that th eincrease in the prime rate could not be "justified" by the usual rules of "supply and demand," but was "a response" to recent action by the Fed designed to restrict the nation's money supply.

"[Banks] have got more liguidity than they ever had, and there's no loan demand to speak of ," Lance charged. He noted that in Washington, some banks were in effect offering loan "sales" by cutting interest rates.

Federal Reserve sources, who refused to be quoted by name, challenged Lance on the facts. They said that there had been a sharp upturn in business loan demand in most parts of the country since Jan. 1.

Lance, formerly a Georgia banker and now President Carter's closest adviser on the conomy, was careful to say that he was not criticizing the Fed, and did not consider that he was engaging in a "confrontation" with Chairman Burns.

Liberal Democratic leaders have expressed strong private opposition to a report that Carter might reappoint the 73-year-old Burns when his term as chairman (but not as a member) of the Fed expires next February.

Burns lately has praised Carter's cautious economic policies, especially Carter's commitment to balance the federal budget in fiscal 1981.

Lance's careful posture yesterday was to question not the wisdom of recent Fed action to tighten up the money supply, following this spring's explosion, but what might be the end result of that action.

"This may well be the time they have to do that (tighten up the money supply), rather than later on," Lance conceded.

But "I'm a low-interest man," Lance told reporters, "and I have no apologies to make for that. I don't think this country does well on high interest rates."

The Fed maintains that it merely has been acting prudently to try to correct a growth in the money supply in March and April that overshot its targets. In April, for example, the money supply (currently and checking accounts) increased at an annual rate close to 20 per cent.

On May 3, in testimony before the House Banking Committee, Burns gave a clear warning that the money growth trend, in his view, had been too rapid. By selling government securities, the Fed proceeded to pull money out of the private economy, reducing bank balances available for loans, and automatically raised short-term interest rates.

What Lance was saying yesterday was that the banks are stuffed so full of cash despite the squeeze place on them by the Fed that they might have absorbed the higher federal funds cost, and kept their own lending rates stable.

But the financial markets see the picture somewhat differently. Although loan demand in most areas of the nation is good, analysts acknowledge that commercial loan demand at the big New York and Chicago banks is slack, due to the ability of blue-ribbon corporations to borrow in the commercial paper market at 150 basis points (1.5 percentage points) below the prime rate.

In effect, it is explained, with their best customers having deserted them, and higher money costs enforced by the Fed, the banks suffered a profit squeeze. The alternative was to try to recoup by raising their lending rates.