...federal courts have ruled that the Fourth Amendment's bar of "unreasonable" searches and seizures limits the president's power to intercept communications without obtaining a warrant. But that doesn't apply to foreign intercepts, as the Supreme Court made clear in a 1972 case, writing, "The instant case requires no judgment on the scope of the president's surveillance power with respect to the activities of foreign powers, within or without this country." The federal courts of appeals for the 5th, 3rd, 9th and 4th Circuits, in cases decided in 1970, 1974, 1977 and 1980, took the same view. In 2002, the special federal court superintending the Foreign Intelligence Surveillance Act wrote, "The Truong court, as did all the other courts to have decided the issue, held that the president did have inherent authority to conduct warrantless searches to obtain foreign intelligence information. ... We take for granted that the president does have that authority and, assuming that is so, FISA could not encroach on the president's constitutional power."
Update – From Justice Byron White's concurrence in the decision of Katz v. United States:
"Wiretapping to protect the security of the Nation has been authorized by successive Presidents. The present Administration would apparently save national security cases from restrictions against wiretapping. We should not require the warrant procedure and the magistrate's judgment if the President of the United States or his chief legal officer, the Attorney General, has considered the requirements of national security and authorized electronic surveillance as reasonable."
Thanks to William Hindman for this find.