Marian Day Miller, 67, who retired from the State Department in 1972 after 36 years of service and who then became an administrative assistant at the National Academy of Sciences, died of cancer Sunday at her home in Arlington.

Mrs. Miller was born in Westford, Mass. She attended Syracuse University, and earned a bachelor's degree in business administration at Simmons College in Boston in 1933.

The following year, she moved to Washington and began her career with the government with the Securities and Exchange Commission. She worked briefly for the Veterans Administration before joining the State Department in 1936.

In 1941, she was assigned to the U.S. Embassy in San Salvador, El Salvador, and remained there for the next 18 years. At the time she was transferred back to Washington, she was the embassy's budget officer. Her subsequent work at State also involved budgets.

After retiring from the government, she went to work for the National Academy of Sciences. She remained there until 1979, when she retired for reasons of health.

Survivors include her husband, Henry, whom she married in 1944, of Arlington; one daughter, Peggy Cummings of Oxford, Me.; a sister Viola D. Robison of Westfield, N.J., and six grandchildren.