The Commissioner of the General Service Administration's troubled federal supply service, which provides federal workers with office supplies, equipment and motor pools, will resign this month, it was learned last night.

Robert F. Graham, a retired senior vice president of citibank in New York who took over GSA's federal supply service 16 months ago, has submitted his letter of resignation, effective Oct. 23, to GSA administrator Jay Solomon.

Although GSA officials said last night that Graham was "leaving of his own free will" and had been "cooperating" with efforts to stop widespread corruption in the supply service, it was known that Solomon wanted someone who could devote more time and vigor to the task.

Graham, who noted in his letter of resignation that he had been "commuting to my home by air every weekend to be with family as much as possible," said he had "instituted many major management reforms, procedures and controls in the federal supply service over the last 16 months . . .

"However," Graham added in his letter to Solomon, "it is evident to me that the successful completion of this effort requires a long-term commitment which I am not positioned to undertake."

Federal investigators, government auditors and inquires by The Washington Post have found long-standing corruption and waste throughout the federal supply service.

Federal prosecutors have found that managers of 27 of the 30 GSA supply stores that provide office supplies to federal workers in the Washington region have accepted bribes from firms selling them the supplies. In return, the GSA store managers allowed the firms to be paid for supplies never delivered. Three GSA store managers and two officers of a supply firm pleaded guilty this week to charges of defrauding the government.

GSA's supply service has also spent hundreds of millions of dollars on faulty desks and filing cabinets, lost millions of dollars in fraudulent charges on GSA-issued credit cards for gas, oil and repairs for motor pool cars, and paid more for office machines than discount store customers or state governments pay for the same items, government audits and inquiries by the Post have revealed.

Graham himself had become a central figure in GSA's recent dealings with Art Metal-U.S.A. Inc., GSA's chief supplier of steel desks, cabinets and bookcases.

Graham's approval of continued GSA purchases of Art Metal's products was overruled by Solomon after the Post reported complaints by federal agencies that Art Metal's desks and file cabinets were not well made and required excessive repairs. Solomon specifically canceled a recent $9.4 million contract with Art Metal for more file cabinets. After reviewing testimony by Graham, among others, a federal judge ruled here yesterday that GSA did not have sufficient evidence to cancel the contract.

Graham is the highest ranking GSA official to leave the agency since the scandals there made front page headlines and the ongoing federal investigations of the agency here and in Baltimore moved into high gear.

In August, GSA Administrator Solomon replaced several officials in the Washington regional office, including the regional supply service commissioner.