An Immigration and Naturalization Service judge yesterday ordered the immediater deportation of England of Gary Davis, former U.S. citizen turned self-proclaimed "World Citzen," on grounds that he is an alien attempting to enter this country without proper documents.

An appeal, however, by Davis' attorney has stayed the deportation order, and Davis remains in custody at the Dulles Marriott Hotel.

Davis' lawyer, David Carliner, took the position at the hearing before Judge Emil Bobek that Davis is not an alien and that United States law permits him to live in this country as a national.

"Although he renounced his citizenship, he did not renounce his allegiance to the United States," Carliner said. "He took an oath of allegiance to the (50,000-member) 'World Government' does not supersede allegiance to the United States."

Carliner said he believes the case would provide a precedent in the controversy about Americans who renounced their citizenship to protest the Vietnam War and who now want to come home.

At the hearing, Carliner said, Davis was offered the opportunity to apply for naturalization under a law that permits this for combat veterans, but the offer was rejected. Davis, who turned in his American passport in 1948, was a bomber pilot during World War II.

Davis, 56, son of the late band leader, Meyer Davis, was arrested at Dulles Airport on May 13 as he returned from England and attempted to present his 'World Passport' to immigration authorities. He remains in the custody of Pan American Airways, the carrier which brought him here, pending payment of a $3,000 bond.

Carliner said England would not accept Davis because his client is not a citizen of that country. He added that when Davis was deported from England in 1953, he was returned to the United States. Carliner said Davis has not lived anywhere permanently since 1948.