NASA Administrator James M. Beggs yesterday took an indefinite leave of absence from the space agency to fight fraud charges against him. With White House approval, Associate Administrator Philip E. Culbertson was named general manager, effectively bypassing newly arrived Deputy Administrator William R. Graham.

Beggs refused to resign, despite scattered calls on Capitol Hill that he quit the post he has held since June 1981. He was indicted Monday on charges that he tried to hide cost overruns on a federal defense contract from 1978 to 1981 as an executive vice president at General Dynamics Corp.

"For the record, I do not intend to leave the agency," Beggs said in a statement issued last night. "This is not an interim step to a resignation."

White House spokesman Larry Speakes said that President Reagan, "while reluctantly acceding to his request for a leave of absence," asked Beggs to assist in an "orderly transition . . . at this critically important agency."

Putting Culbertson in charge of day-to-day operations was Beggs' stamp on the transition. Culbertson, 60, is a 20-year NASA veteran, well-known to the House and Senate committees that deal with the agency. Culbertson has been planning the space agency's next big project, the construction of an $8 billion permanent space station as early as 1992.

Graham, 48, a former planning analyst at the Rand Corp. and chairman for the last three years of the White House Advisory Commission on Arms Control and Disarmament, has been with NASA eight working days. Reagan appointed Graham acting administrator, so that Graham could create the new job of general manager and name Culbertson to the post.

". . . I think this is a very acceptable plan in light of the ordeal Jim Beggs is going to have to go through," said Rep. Don Fuqua (D-Fla.), chairman of the House Committee on Science and Technology. "The year ahead is a pivotal year for NASA and Phil Culbertson has been there long enough to know the agency and the issues he'll be involved with."

The agency's most pressing concern is funding for the permanent space station. NASA received $205 million of the $230 million it requested for the project in fiscal 1986 is expected to ask for $600 million in fiscal year 1987 and $1 billion in fiscal year 1988 to stay on schedule.

"Whoever is running the space agency in 1986 has to know where the space station stands, what money it needs and who to talk to to keep it on track," said a congressional aide who deals with NASA. "That's why Phil Culbertson is getting the job of running the agency day-to-day. He knows the issue."

NASA also faces an unforgiving launch schedule in 1986 that includes 14 shuttle flights and three expensive and ambitious unmanned missions to explore Jupiter, the sun's north and south poles and the edge of the observable universe.

Next May, two shuttle flights are scheduled in one week to launch a German-American spacecraft named Ulysses on a roundabout journey toward the sun and a Galileo spacecraft toward Jupiter. Next August, NASA is to launch the $1.2 billion Space Telescope, the most expensive instrument ever placed in space, to study the far distant parts of the universe.

"I think it will probably be the most important year we've ever had," Beggs said not long ago, "including the halcyon days of the manned Apollo landings on the moon."

In his statement, Beggs reiterated that he is innocent of the fraud charges resulting from a Justice Department investigation. General Dynamics, Beggs and three company officials were indicted in connection with cost overruns on an Army contract to develop a prototype of the Divad antiaircraft gun.

"I have concluded there was nothing I did then that I would not do again," Beggs' statement said. "I have not been involved in any criminal wrongdoing or, in fact, of wrongdoing of any kind. I am totally confident I will be exonerated."