Condemning mosque, Gingrich echoed apocryphal Mussolini line [UPDATED]

A regular correspondent wondered why Newt Gingrich's recent declaration on the planned downtown mosque sounded so familiar, and found this:

Gingrich:

There should be no mosque near Ground Zero in New York so long as there are no churches or synagogues in Saudi Arabia.

Mussolini:

There will be a mosque in Rome, the Fascist ruler said, only when a Roman Catholic church is permitted in Mecca.

The quote is frequently attributed to Il Duce, though I'd be grateful to any Italian-speaking reader who has a primary source.

UPDATE: The Mussolini line, though widely reported, appears to be apocryphal.