The Carter administration has targeted 304 government advisory committees for extinction, but President Carter, dissatisfied with that initial recommendation, has ordered his Cabinet secretaries and agency heads to find other committees that can be eliminated.

"I believe more can be done . . .," the President said in a memorandum sent to executive departments and agencies this week.

White House and Office of Management and Budget officials were debating yesterday whether to make an early announcement of which committees are on the initial target list. Once the list becomes public, they anticipate a flood of protests and lobbying efforts by individuals and interest groups seeking to preserve some of the committees.

The advisory committees vary widely, ranging from the Agriculture Department's Advisory Committee on Hog Cholera Eradication to the Veteran's Administration's Chief Medical Director's Ad Hoc Advisory Committee on Spinal Cord Injury.

What they share in common is that they are made up of people outside the government who are up to $184 a day, plus travel expenses to meet and offer government agencies advice on matters ranging from broad policy issues to narrow technical and scientific questions.

OMB officials estimate that this costs the government $65 million a year and involves some 25,000 individuals serving on 1,189 advisory committees.

Last February, the President ordered each agency to review the committee reporting to it and to reccommend which could be done away with. The initial list of 304 - representing 26 per cent of the total - is the result of that first review by the agencies.

OMB is keeping its own scorecard on the agencies' performance. It shows that the Agriculture Department has been the most aggresive in seeking to root out unnecessary committees. Those showing the least inclination in this direction are the Commerce, Labor and Interior Departments, according to the OMB scorecard.

The Africulture Department has recommemded doing away with 89 advisory committees, repsenting 81 per cent of the 110 committees serving it. The Commerce Department on the other hand, proposed elimination of six committees, representing 7 per cent of its total of 91.

The Labor Department said it could do without three of its 25 committees (12 per cent) and the Interior Department seven of its 49 committees (14 per cent).

The Department of Health, Education and Welfare recommended the largest cut in terms of numbers of committees - 91. But HEW also begins with the largest number, 352, so the cut would total 25 per cent, the average for the government as a whole.

Among independent agencies, the Export-Import Bank proposed doing away with its lone advisory committee, a 100 per cent performance in OMB's view. But the National Science Foundation said it could get along with only two less than its current 55 advisory committees, while the Federal Energy Administration - itself targeted for extirnction in the pending Energy Department legislation - proposed eliminating only one of its 14 committees.

OMB officials said they are now going to take the initiative and begin reviewing the reasons why the agencies wish to continue with 876 adivisory groups. For some, extinction could be as simple as a presidential or agency order wiping them out. But for an estimated 20 per cent of the total, including about 30 on the initial target list, legislation will be necessary to end their existence.