President Carter yesterday signed legislation that gives him the authority to reorganize the federal government, which he noted was "the most consistent commitment" he made during his campaign.

The first target of reorganization will be the executive office of the President, which includes the White House and 17 support agencies such as the National Security Council and the Council of Economic Advisers.

Bert Lance, director of the Office of Management and Budget, said a plan to reorganize the executive office is expected to be submitted to Congress in June.

But in a briefing for reporters, Lance downplayed the importance of reducing the number of federal agencies, whicn Carter once boasted would be a major benefit from reorganzation.

During the campaign, the President promised to cut the number of federal agencies from the some 2,000 that now exist to about 200. Hamilton Jordan, a top White House aide, has since admitted that the number 200 was totally arbitrary, arrived at without much thought.

"I don't think we should say we will cut the number to 200," Lance said in response to a question yesterday. "Numbers are on measure, but they shouldn't be the prime measure. I don't think we should play the numbers game."

Lance also shield away from suggesting that the net result of the three-year reorganization process would be a net reduction in the cost of government.

Asserting repeatedly that he did not want to "pre-judge" the course reorganization will take, Lance said one of the main goals of the effort will be to "fix accountability and responsibility" in the government, thereby making it more efficient and responsive.

The legislation the President signed yesterday, surrounded by members of Congress in the traditional ceremony, gives him authority for the next three years to submit reorganization proposals to Congress. The proposals would automatically take effect unless vetoed by either house of Congress within 60 days of their submission.

The reorganization authority has limits. Under it, for example, Carter cannot abolish Cabinet departments or create new ones. Thus, he has submitted separate legislation to Congress that would create an energy department.

In keeping with the importance the President places on reorganization, the White House released two documents on the subject. Although Lance said the administration has not decided which areas of government will undergo reorganization studies first, one document said areas targeted for early action include energy, oil spill pollution control, consumer affairs, civil rights and advisory committees.

The documents also said that the reorganization effort will include "a major study of the Civil Service Commission," and that as a result or reorganization "the average citizen . . . can anticipate the efficiency and quality of government service will be improved."

Those who attended the ceremony included House Government Operations Committee Chairman Jack Brooks (D-Tex.), who waged a vocal but ineffective fight against the type of reorganizating power the President won. Carter greeted Brooks warmly and singled him out for praise.