President Reagan, under fire from Congress for padding his staff with employes carried on departmental payrolls, will reimburse agencies for the detailees' salaries starting in October, a White House spokesman said yesterday.

The General Accounting Office reported in July that the White House had augmented its staff with 349 employes on "detail" from Cabinet departments during the first five years of the administration.

The GAO said that the administration, in many cases, had failed to reimburse the parent departments or report the detailees to Congress, as required by law.

Ben Jarratt, assistant White House press secretary, dismissed GAO's charges yesterday as a "differing interpretation" of the law.

"Nevertheless, out of an abundance of caution . . . we will report employes detailed . . . and will reimburse a detailing agency for the services performed in excess of 180 days," he said.

An aide to Rep. Fortney H. (Pete) Stark (D-Calif.) said, "They get their hand slammed in the cookie jar and even after they get caught they won't admit anything, they just reluctantly replace the cookies."

Jarratt said that reimbursement will begin in the upcoming fiscal year through "belt-tightening and careful management."

The GAO cited numerous cases in which a detailee was hired at the direction of the White House without ever setting foot in the employing agency.

The GAO said that since 1981, one woman has been promoted five grades in the Interior Department while working full time in the White House personnel office.

The woman -- who is listed as the No. 2 official in the White House personnel office as Maureen Zatarga, and on documents released under the Freedom of Information Act by GAO as Mary Zatarga -- was sent to the White House under an arrangement worked out with then-Interior secretary James Watt, according to the GAO files.

Zatarga declined comment and referred calls to Jarratt.

According to the GAO, she was appointed as a GS-9 confidential assistant to the assistant secretary of interior for territorial and international affairs.

"The position description submitted to the {Office of Personnel Management} stated that the incumbent's primary function was to devise ways and means of relieving the assistant secretary in every possible way and personally handle many matters without referring them to him," the GAO said.

Five months later she was promoted to a GS-11, stating "she was responsible for keeping abreast of the political situations in Guam, American Samoa, the Virgin Islands and the Trust Territories of the Pacific Islands," the GAO said.

In 1985, Interior waived rules that Zatarga serve a minimum number of years in grade, and also waived qualification requirements to promote her two grades to a GS-13. The justification stated, according to the GAO, that "Ms. Zatarga handles a wide variety of highly confidential and complex assignments . . . . "

Last April, according to the GAO, she was promoted again, to a GS-14, which is equivalent to the rank of a division chief in many bureaus of Interior. In documentation sent to OPM, she was reported to be working for Interior.

Kittie Baier, the acting assistant secretary for territorial and international affairs and former confidential assistant to Watt, declined comment yesterday on the case.

Jarratt said the White House had "instructed the personnel office to work more closely with its counterparts in the agencies to ensure that the performances of their detailees are properly documented."