Carl Bernstein reported on this several years ago in Holy Alliance. Take a look at it - a very interesting read.
One paragraph from this article:
The key Administration players were all devout Roman Catholics--CIA chief William Casey, Allen, Clark, Haig, Walters and William Wilson, Reagan's first ambassador to the Vatican. They regarded the U.S.-Vatican relationship as a holy alliance: the moral force of the Pope and the teachings of their church combined with their fierce anticommunism and their notion of American democracy. Yet the mission would have been impossible without the full support of Reagan, who believed fervently in both the benefits and the practical applications of Washington's relationship with the Vatican. One of his earliest goals as President, Reagan says, was to recognize the Vatican as a state "and make them an ally."