The Reagan administration underestimated federal spending in fiscal 1982 by $3 billion to $6 billion in the budget presented to Congress last week, White House aides said Yesterday.

The discovery of the underestimates perils the budget assumptions on which President Reagan said his administration would rein in federal spending to an annual growth rate of 6 percent and balance the budget by 1984.

Reagan expressed concern and ordered Office of Management and Budget Director David A. Stockman to review the entire budget to find new spending reductions that will bring budget totals back into line with the message he delivered to Congress and the American people.

"The president is firmly committed to the basic order of magnitude he set down Feb. 18," domestic adviser Martin Anderson told reporters.

In a separate development, White House aides have been telling interested people that the decision to eliminate the 10-yea-old Council on Environmental Quality has been made. Rep. John B. Breaux (D-La.), chairman of the House fisheries subcommittee on conservation and the environment, promised a fight over the presidential advisory body. The Carter budget sought $3.7 million for CEQ.

The immediate problem facing administration budget-cutters is to identify enough spending cuts by March 10 to enable Reagan's promised second message to Congress to explain where all the spending reductions will be made. m

Even before the underestimates were made public by the white House, Democrats in Congress had seized upon the fact that Reagan's first message left $6.6 billion of his promised $41.4 billion in cuts unidentified. Several warned against approving the spending cuts before knowing the entire program in detail.

Now, Stockman and his office must find between $9.6 billion and $12.6 billion in further cuts in time for the March 10 message.

Anderson said Reagan "expressed concern, but not surprise" when Stockman told him of the underestimates. "He's used to budget numbers going the wrong way," Anderson added.

It is crucial to the budget projections of the Reagan administration that the fiscal 1982 budget be held to the $695 billion total with a $45 billion deficit that Reagan announced last week. If those goals are not met, Reagan will also fail to make good on his promises for distant future, including a balanced budget in 1984.

What caused the underestimates is apparently the same inexorable pressures for higher spending totals that ballooned former president Carter's budget for the current year -- more than doubling the projected deficit between June and November -- and damaged his chances for reelection.

Reagan aides said the distinction between his handling of the problem and Carter's is that Reagan quickly ordered new budget cuts to try to keep spending under control.

The decision to go public with the underestimates was made yesterday afternoon at a meeting attended by counsellor to the president Edwin Meese III, White House chief of staff James A. Baker III, Anderson, White House press secretary James S. Brady and presidential assistant David Gergen. They feared that word of the underestimates would leak since Reagan had informed his Cabinet members.

After consultation with Stockman, they decided to announce only that the total was "several billion dollars." Anderson spent some uncomfortable minutes refusing to say whether "several" meant more or less than $10 billion.

Gergen confirmed that the range of the underestimates is $3 billion to $6 billion. "It's my understanding from the people at OMB that this is the range we're dealing with, but it may go up slightly or it may come down a bit." OMB had been reluctant to make the range public because of the possibility the numbers will change again.

Dale MacOmber, OMB assistant director for budget review, said the numbers on which the first Reagan Calculations had been made were two and a half to three months old. He told reporters that revisions like this one happen constantly.

Anderson said that although new budget cuts are needed, the seven programs Reagan has called the "social safety net" are still immune from cuts. Anderson also excluded the possibility that any new taxes like the discussed 2-cent-a-gallon increase on gasoline are being contemplated to close to budget gap.

Anderson said the underestimates were uncovered when OMB went back to all government departments and agencies and asked for updated totals of their spending projections. To compile the Feb. 18 budget numbers, the Reagan administration had relied basically on numbers in the Carter budget and subtracted the totals of the cuts it had decided to make.