President Reagan, after months of sniping at the Federal Reserve Board, switched tactics yesterday, praised the Fed's tight money policy and offered friendly cooperation with the central bank to reduce interest rates and inflation.

In a prepared statement opening his news conference, Reagan, who met with Federal Reserve Board Chairman Paul A. Volcker Monday, pointedly moved to make peace, making no mention either of past administration unhappiness with Fed policy or the Fed chairman's recent criticism of the Reagan budget.

Administration officials have recently blamed the Fed for the high interest rates now pinching the economy, suggesting the board was not letting the money supply grow smoothly enough. Volcker has suggested instead that the Reagan deficits are to blame, that rates are being driven up by government borrowing.

Yesterday Reagan played down this conflict. "I have confidence in the announced policies of the Federal Reserve Board. The administration and the Federal Reserve can help bring inflation and interest rates down faster by working together than by working at cross purposes," he said.

At the eighth White House news conference of his presidency, Reagan also:

Defended B. Sam Hart, the Philadelphia black evangelist he has nominated for a seat on the U.S. Civil Rights Commission.

Refused to name a month for the start of the economic recovery his administration has predicted. Aides have said it will start this spring.

Maintained his strong position against raising taxes or cutting defense spending to reduce the fiscal 1983 deficit.

Announced he will set up a new task force to be run by private citizens and paid for by private funds to find ways to control federal costs.

Refused to discuss U.S. military options in El Salvador or say whether he has authorized covert operations to destabilize the government of Nicaragua (details on Page A5).

In pledging cooperation with the Fed, the president--whose budget calls for a $91.5 billion deficit in fiscal 1983--spoke out against large deficits.

Reagan said he "fully supports" the Fed's 1982 money growth targets, as "fully consistent with the administration's economic projections for the coming year." At the same time, he promised to "devote the resources of my presidency to keeping deficits down over the next several years."

Many outside economists say the Fed's money growth targets are too low to accommodate simultaneously the private economic growth and federal budget deficits Reagan is projecting. Volcker was sharply critical of the size of Reagan's projected budgets in several public statements last week.

The president said that current high interest rates reflect concerns that the Fed will "revert to the inflationary monetary policies of the past" on the one hand, or that his administration will tolerate increasing budget deficits on the other.

In a statement apparently meant to reflect his most recent meeting with Volcker, Reagan said, "I want to make it clear today that neither this administration nor the Federal Reserve will allow a return to the fiscal and monetary policies of the past that have created our current conditions."

On his budget, Reagan acknowledged that he had received little initial support fron members of Congress, but said he hopes attitudes will be softened by contact with voters over the present recess. "I think there is widespread support for continued cutting of government spending," the president said.

The president said he is willing to consider alternatives to his budget, but that all he has heard from opponents is "diatribe, opposition and criticism."

He said his basic tax program is vital to his promised economic recovery, but that he will agree to close loopholes through which people escape "a legitimate tax burden they should pay."

"I'm not going to be pinned down on a date," Reagan said when asked when the recovery will come. Another reporter reminded Reagan that he and his senior advisers have repeatedly said the recovery would come around June. He again refused to mention a month, but insisted that his caution did not represent a change in his position on the recovery.

The president defended Civil Rights Commission nominee Hart, saying "I am quite confident in his quality and his ability for that job . . . ."

The president corrected a questioner who misstated Hart's position on women's rights. "He specifically stated that he is for equal rights for women. He just happens to be opposed to the ERA Equal Rights Amendment as a method of getting them." With a smile, Reagan noted that he takes the same position.

The president noted that Hart opposes busing to desegregate schools and said that position is supported by a majority of blacks and whites across the nation.

In reply to another question, Reagan said he could not believe that his aides permanently refused to schedule an appointment with him for 42 members of Congress concerned about farm problems. "Maybe they couldn't okay the meeting at the time they the members of Congress wanted it."

However, Reps. Byron L. Dorgan (D-N.D.) and Thomas A. Daschle (D-S.D.) and the other 40 signers of the request did not suggest a time for the meeting. They simply asked to see the president.

The Feb. 9 White House reply signed by Gregory Newell says only "it is not possible to arrange such a meeting at this time."

Reagan told another questioner that despite cutbacks in student loan programs no student "with true need" will suffer.

The president fulfilled a campaign promise by announcing to his news conference that he will set up a private sector task force to study ways of controlling federal spending. Its members will be charged with finding waste and inefficiency in the government and will report to the president, Reagan said.

The group will be established as a 501(c)(3) charitable organization which means that contributions to it will be tax deductible. The executive committee of the task force will consist of leaders from business, labor and universities. The operating committee will be headed by James W. Nance, former deputy director and acting head of the National Security Council. "Government assistance and involvement will be minimal," the White House said.

Reagan said the new group will first study the departments of Defense, Health and Human Services, and Housing and Urban Development.