The Navy and the Defense Department said yesterday they want to appeal a federal judge's decision ordering Navy Secretary John F. Lehman Jr. to expunge an official censure from the record of a former Marine Corps colonel accused of cooperating with the North Vietnamese while a prisoner of war.

The Navy said the censure, issued in 1973 by then Navy Secretary John Warner, now a Republican U.S. senator from Virginia, "was fully warranted" and that the "time-honored inherent authority of the secretary to censure subordinates is an integral part of Navy leadership that must be preserved."

U.S. District Judge Gerhard A. Gesell ruled Monday that Warner's censure of the former colonel, Edison W. Miller, now 53 and a lawyer in southern California, was "manifestly a case that 'shocks the sense of justice' " because the retired officer was not given the specifics of the charges against him and was denied access to investigative reports and the names of adverse witnesses.

The Navy and Defense asked the Justice Department to appeal Gesell's ruling. Royce C. Lamberth, head of the civil division in the U.S. attorney's office here, said it is likely that the ruling will be appealed, "but no final decision has been made. It in effect is a court opinion saying that the secretary of the Navy can't reprimand an employe."

"They're using the power of the government to grind me down," Miller said of the Navy's desire to appeal. "I'll figure out a way to fight them every step of the way."