In 1960, Cooper was re-elected, securing his first full, six-year term in the Senate. Newly elected President John F. Kennedy – Cooper's former Senate colleague – chose Cooper to conduct a secret fact-finding mission to Moscow and New Delhi. Following Kennedy's assassination in November 1963, President Lyndon B. Johnson appointed Cooper to the Warren Commission to investigate the assassination. Cooper soon became an outspoken opponent of Johnson's decision to escalate U.S. military involvement in the Vietnam War, consistently advocating negotiation with the North Vietnamese instead. After Cooper's re-election in 1966, he worked with Idaho Democrat Frank Church on a series of amendments designed to de-fund further U.S. military operations in the region. These amendments were hailed as the first serious attempt by Congress to curb presidential authority over military operations during an ongoing war. Aging and increasingly deaf, Cooper did not seek re-election in 1972. His last acts of public service were as Ambassador to East Germany from 1974 to 1976 and as an alternate delegate to the United Nations in 1981. He died in a Washington, D.C., retirement home on February 21, 1991, and was buried in Arlington National Cemetery.