The Senate rapidly approved 10 of President Carter's top nominees to Cabinet and economic posts yesterday, but temporarily withheld action on three others because of objections from various senators.

The nomination of Griffin B. Bell as Attorney General will not be taken up until next week because of objections from Sen. Edward W. Brooke (R-Mass.) and other civil rights advocates who want time to study the full record over the weekend.

The nomination of Joseph A. Califano as Secretary of Health, Education and Welfare will be voted on Monday. It was delayed because Sen. Robert W. Packwood (R-Ore.) wanted an opportunity to express his opposition to Califano because the nominee opposes federal funding of abortion for low-income owomen. Sens. Paul Laxalt (R-Nev.), Orrin G. Hatch, (R-Utah) and others also requested a delay until next week on Secretary of Labor nominee F. Ray Marshall because of Marshall's strong union views.

Approved yesterday were Cyrus R. Vance as Secretary of State; W. Milchael Blumenthal, Secretary of the Treasury; Harold Brown, Secretary of Defense; Cecil D. Andrus, Secretary of the Interior; Bob Bergland, Secretary of Agriculture; Juanita M. Kreps, Secretary of Commerce; Patricia Roberts Harris, Secretary of Housing and Urban Development; Brock Adams, Secretary of Transportation; Thomas B. (Bert) Lance, director of the Office of Management and Budget, and Charles L. Schultze, chairman of the Council of Economic Advisers.

Sen. William Proxmire, (D-Wis.) objected to Lance, saying he lacked sufficient experience for a job which requires a thorough knowledge of the federal budget and programs. Proxmire also voted against Harris, saying she lacks experience in housing. And he said that while he was voting for Brown, he wanted to caution him to remember that President Carter had expressed opposition to the B-1 bomber, support for a $5 billion to $7 billion defense cut and reinstatement of A. Ernest Fitzgerald, the defense official who exposed C-5 plane overruns.

He said that Brown as Secretary of the Air Force had apparently disciplined Fitzgerald in 1968 and appeared to be less than clear in his backing of what Proxmire described as Carter's position on defense cuts.

The Senate agreed to begin debating the Bell nomination Tuesday with an eight-hour time limitation, but William L. Scott (R-Va.) blocked any time limit on Marshall.

Robert J. Havel, spokesman for the Justice Department said that under an order signed earlier this week by outgoing Attorney General Edward H. Levi, Assistant Attorney General Richard L. Thornburgh will become acting head of the Justice department until action is completed on the Bell nomination.

Although Deputy Attorney General Harold R. Tyler Jr. and Solicitor General Robert H. Bork also submitted resignations effective yesterday, Havel noted that their resignations had not been formally accepted. As a result, he said, it is possible that the White House might ask one of them to take over as acting Attorney General.