The cable castigated President Diem’s brother, Ngo Dinh Nhu, the head of South Vietnam’s security forces, for attacking pagodas of the country’s Buddhist majority under martial law. Reflecting White House fears that Mr. Nhu’s brutality could turn popular sentiment toward the Communists, the cable told Mr. Lodge to tell the Mr. Diem to get rid of Mr. Nhu. At the time, the United States had 16,000 military advisers in Vietnam.

“If in spite of all your efforts, Diem remains obdurate and refuses, we must face the possibility that Diem himself cannot be preserved,” the cable said. Mr. Lodge, it said, “should urgently examine all possible alternative leadership and make detailed plans as to how we might bring about Diem’s replacement if this becomes necessary.”

The cable, which was made public in later years by the National Security Archive, was approved by President John F. Kennedy but written with some urgency on a Saturday, when he, Vice President Lyndon B. Johnson and other senior officials were all out of town. Military officials were angry that they had been bypassed, according to Mr. Hilsman’s own records, now housed at the John F. Kennedy Library.

Mr. Diem and his brother were killed in a coup by South Vietnamese generals in early November 1963, and it ushered in a period of political instability in Saigon that many historians believe led to an increase in American involvement in South Vietnam’s war with Communist North Vietnam and its South Vietnamese allies, the Viet Cong.

In a 2010 interview with CNN, Mr. Hilsman insisted that Kennedy would not have escalated the war had he not been assassinated later that November. “From the beginning he was determined that it not be an American war,” he said.