In 1975, President of the United States Richard Nixon appointed Murray as Deputy Assistant Secretary of Defense (Manpower and Reserve Affairs), a post he held until 1976.
In 1978, President Jimmy Carter appointed Murray as Deputy Assistant Secretary of Defense (International Security Affairs).
During this period, he participated in Carter's negotiation of the Camp David Accords between Israel and Egypt.
He first joined the Naval War College in Newport, Rhode Island in 1981 as Dean of the newly established and Center for Naval Warfare Studies and first director of the Strategic Studies Group.
[2] After his retirement from teaching, Murray served as president and chief executive officer of CNA.