He could assert executive privilege and then the court would decide the issue. Executive privilege, much like sovereign immunity, covers two realms, the communication privilege and the deliberative process privilege. The communications privilege is essentially the protection of the executive branch against unwarranted intrusion by the other branches of government, rooted in separation of powers.
The deliberative process privilege is similar to what might have applied in 1789 when the Constitution was drafted, i.e. rooted in common law privileges inherited from England.
And the privilege, much as sovereign immunity, covers two times, when the President is actually sitting, when it is general and attaches to the person, and retroactively, to any acts while acting as President, which does not go away when the person is no longer in office. Otherwise, the national security and other purposes the privilege serves would be immediately defeated the instant anyone left office.
And specifically, the deliberative process privilege is seen as easier to defeat by common law privileges. When the President is sitting, the privilege protects the decision making process the President is using and this has national security implications for the future. If the court ruled the stronger communications privilege didn't apply, and analyzed it on deliberative process privilege, the privilege would be less because it would not as strongly impact future events. It might, however, still chill what decisions or processes future Presidents might use, or compromise intelligence methods still in use.
In any event, it would be up to a court (and probably ultimately the Supreme Court) to decide the issue if it comes to it.
