The mysterious U.S. emissary given credit by Libyan leader Muammar Qaddafi for defusing U.S.-Libyan military tension in January turns out to have been the U.S. ambassador to the Vatican, William A. Wilson.

Administration sources said last night that Wilson had made an unauthorized visit to Libya in early January, about the time that Qaddafi told NBC's "Meet the Press" while seated on a tractor in a barley field outside Tripoli that an American emissary had helped eliminate the possibility of military confrontation.

At the time, White House and State Department officials said they knew of no such U.S. diplomatic contacts and suggested that Qaddafi was guilty of fictional diplomacy or at best gross exaggeration.

Wilson's unauthorized diplomatic venture, which came to light later, brought a reprimand from Secretary of State George P. Shultz, according to officials.

The tensions with Libya stemmed from Qaddafi's alleged connection with terrorist attacks on the Rome and Vienna airports on Dec. 27. Some officials in the administration urged retribution for the airport attacks, but President Reagan ruled out retaliatory action.

The United States, however, is now sending three aircraft carriers and 27 warships toward Libya's Gulf of Sidra, and administration sources have said that some ships and U.S. jet fighters will cross within the next 10 days or so a "line of death" that Qaddafi has drawn across the gulf.

Wilson, a millionaire southern California investor who was a member of Reagan's "kitchen cabinet" in 1980-81, has been noted for independent diplomacy that has been irritating to the U.S. Embassy in Rome and occasionally to the State Department. But the Libyan venture, first reported in The New York Times today, was his most serious breach of diplomatic instructions so far in the eyes of administration officials.

Shultz will have a chance to discuss Libyan diplomacy and other subjects with Wilson next weekend when the secretary of state and his wife stop at the Vatican for Easter services during Shultz's current European trip.

Last night, State Department spokesman Peter Martinez said, "There have been no contacts authorized between U.S. officials and Qaddafi or his regime."

This was the same statement made on Jan. 6, the day after Qaddafi claimed, and Washington denied, discussions with the U.S. administration through the unnamed emissary.