Robert T. Webber, 56, a retired State Department official , died of cancer Monday at George Washington University Hospital.

He was director of the office of atomic energy affairs at the State Department from 1973 until retiring in 1975.

Mr. Webber joined the department in 1962, and was assigned to Tel Aviv as scientific attache until 1966, when he held a similiar position in Tokyo of space, atmospheric and marine sciences at the State Department here during 1970-73.

Born in Newton, Mass., Mr. Webber was a graduate of Amherst College. He taught in the department of physics at Yale University during 1943-49, and earned mater's and doctoral degrees from Yale.

From 1949 until 1957, he was head of the cryogenics branch at the Naval Research Laboratory here. He then spent three years in London as deputy scientific director of the Office of Naval Research.

Mr. Webber was chief scientist of the Tokyon liaison office of the National Science Foundation from 1960 until joining the State Department. He held the Superior Service Award of the department.

The author of numerous research papers, he was a fellow of the American Physical Society and the London Physical Society and a member of the Washington Academy of Science and the American Association for the Advancement of Science.

He is survived by his wife, Clytie of the home in Washington, and a brother, John, of Falls Church.