Dr. Peter Bourne, former adviser to President Carter, today accepted a public reprimand from state officials here for writing an improper drug prescription in July.

Georgia's Composite State Board of Medical Examiners admonished Bourne "that this is an offense which cannot be tolerated." Any future violations of the Georgia Medical Practice Act, under which Bourne holds a medical license, "will be dealt with sternly," the board said in its order.

"It was the board's feeling that his infraction did not warrant a penalty as severe as suspension or revocation of his license," said Dr. Robert Thompson, president of the 10-member medical board. "This was a step just under suspension."

Bourne lost his White House job because of public and political reaction to the prescription he wrote for QUAALUDE, A TRANQUILIZER, FOR ELLEN J. METSKY, A COWORKER IN THE WHITE HOUSE.

HOWEVER, TO PROTECT THE CONFIDENTIALITY OF METSKY, BOURNE SAID, HE USED THE FICTITIOUS NAME OF SARAH BROWN.

BOURNE COULD NOT BE REACHED FOR COMMENT TODAY. BUT HE SIGNED THE ORDER ACCEPTING THE REPRIMAND OF THE MEDICAL BOARD, THUS AVOIDING A FORMAL HEARING ON THE MATTER.

BOURNE'S LICENSE TO PRACTICE MEDICINE IN GEORGIA IS NOT ADVERSELY AFFECTED BY THE REPRIMAND. HE IS LICENSED IN WASHINGTON, D.C., Colorado and California as part of a reciprocal agreement between medical authorities in Georgia and officials in the other jurisdictions.

Quaalude is a federally controlled substance, and a doctor using false name for a patient when prescribing it is acting illegally. However, federal law enforcement officials have said they will not prosecute Bourne, and officials in the jurisdictions in which he is licensed also say they will not take any action against Bourne, a psychiatrist.