Federal Reserve Board Chairman Arthur F. Burns yesterday told the administration and Congress, in effect, to keep their hands off the Fed, which he said would continue to resist pressure from critics to reduce interest rates.

He said the central bank rejects the criticism that it has allowed short-term interest rates to climb too fast. A shift to a policy of mometary ease, he said, would trigger "fears of a new wave of inflation."

Burns assailed efforts to "reform" the Federal Reserve system as a disgised attack on the Fed's independence. Appealing for public support in a commencement address at Jacksonville University, Jacksonville, Fla., Burns said that an erosion of the Fed's independence would limit its ability to maintain "a meaningful anti-inflation posture."

Burns is known to be particularly bitter about legislation introduced by Rep. Henry S. Reuss (D. Wic.), chairman of the House Banking Committee, that would formalize the procedure under which the Fed now gives Congress quarterly targets for monetary growth.

Reuss initially demanded that the Fed also supply targets for interest rates and for the "velocity" (turnover of money. A public condemnation by Burns, suggesting that this would feed speculation and unsettle financial markets, persuaded Reuss to withdrew those proposals.

Burns yesterday did not mention Reuss by name. But he said the "common objective" of proposals "that would place the system under tighter rein" is "to reduce the Federal Reserve's independence and to restrict its scope for discretionary action."

Burns, whose reappointment as chairman at the end of his term next Jan. 31 will be a touchy political economic decision for President Carter, was more oblique in referring to alleged executive department interference with the Fed's independence.

But he said that the degree of independence for the central bank had been a "source of frustration" to some government officials from the beginning. He continued.

"Certainly, from the standpoint of the executive branch, it would at times - perhaps often - be more convenient to instruct the central bank what to do than reckon with the system's independence. In the end, the country would not be as well served."

Currently, there is some feeling in the Carter administration that the Fed is allowing short-team interest rates to creep up too fast, potentially inhibiting economic recovery. Some advisers close to Carter are know to be dead set against Burns' reappointment. But the President, in making his decision, will have to reckon with the hard-to-assess "confidence" factor within the business community.

Without a direct reference to the Carter administration. Burns told the jacksonville graduates that there is a strong "element of populism" among Fed critics pre-occupied with maintaining low interest rates. And as he has repeatedly in congressional testimony this summer, he said the Fed has not intention of loosening the money strings.

"The Federal Reserve system. I assure you," he declared, "will not be deterred by the drumbeat of dubious propositions concerning money and interest rates."

He said the central bank "seeks earnestly" to support governmental policy, but "occasionally" departs from it because "the system tends to take a longer range view of the nation's welfare."

The 73-year-old chairman has rarely been as explicit in outlining what he suggests is a unique relationship between the independence of the Fed and its ability to control inflation.