The Air Force urged the U.S. Court of Military Appeals yesterday to allow the court-martial of 2nd Lt. Christopher M. Cooke to continue despite his contentions that he was promised immunity from prosecution.

"There is a strong public interest in the prosecution of this case," Air Force lawyers asserted in a 72-page pleading filed late yesterday afternoon. "The petitioner Cooke has committed heinous acts which have substantially risked the lives of all of us."

Cooke, 26, a former Titan missile officer, is charged with unauthorized visits to the Soviet Embassy here and with passing information to the Soviets.

Portions of the document made public did not detail how Cooke had risked lives, but the Air Force maintained that assurances given to Cooke during interrogation by Air Force investigators last May were "the result of a misunderstanding" and should not be held as a bar to prosecution.

The Air Force lawyers, Col. James P. Porter and Capt. Michael J. Hoover, noted that one member of the three-judge appeals court had expressed the view at an earlier hearing that the charges should be dismissed. That judge suggested a dismissal was necessary to ensure that similar promises could be relied upon in the future by "those who are asked to provide information," as Cooke was.

Such reasoning, the Air Force lawyers said, "strikes us as unsound." When Air Force investigators gave Cooke the assurances, they "were uncertain whether Cooke had compromised any material at all," the Air Force said.

The soundest avenue in this case, the Air Force lawyers argued, "is to adhere to a rule that an immunity does not exist" unless properly authorized.

Beyond that, the Air Force argued strenuously that "what Cooke has done to national security" was an "equitable factor" in favor of prosecution that the court could legitimately consider.

"We do not think we understate the facts when we say that Cooke's actions have directly impacted on the national security in the most serious way imaginable," the Air Force declared. "The specifics of how and why will have to await oral argument because of its sensitive nature and top-secret classification."