Presenting out-of-competish “W.E,” her first full-length directorial feature, Madonna took the Venice mass media by storm Thursday.

Journalists formed a rugby scrimmage to get into one of the most-packed press conferences in recent years — only to discover they’d battled their way into the Q&A for “Summer Games,” one film before “W.E.” in the presser sked.

Dressed in a sober black frock with period flourishes which wouldn’t have looked out of place on Wallis Simpson, Madonna arrived to whooping enthusiasm from one part of the hall who gave her a standing ovation.

“W.E.” narrates a parallel story in which a Manhattan divorcee (Abbie Cornish) obsesses about the love story between Edward VIII (James D’Arcy) and Simpson (Andrea Riseborough) from the latter’s POV.

Early critics’ responses to the film were less than enthusiastic.

But while Madonna came to Venice to talk about “W.E.,” many scribes attended the presser to ask about a global entity: Madonna.

So questions ranged from the obvious to out-there personal.

What first attracted Madonna to the story of “W.E.”?

“I was deeply and utterly swept up by the reasons why Edward VIII would give up the throne, relinquish his great position of power, for love.”

Would Madonna give up her throne for a man or woman?

“I’d give it up for both, or all three.” (Laughter, cheers)

“How long have you worked on this movie”?

She researched “W.E.” for seven years, and wrote with Alek Keshishian for three, Madonna answered.

How did Madonna handle her spiritual path?

“When you make a film, you have to have strength of mind and karma and soul.”

As with any director’s film, multiple personal references can be read into “W.E.” Madonna wanted to make the point, she said, that “no matter how beautiful and glamorous your surroundings, it doesn’t mean you’re guaranteed happiness.”

There were moments of candor: Madonna admitted “W.E.” was “a really big project for me to take on.”

But the press conference with Madonna ended up being about Madonna. As a last question, key cast were asked their opinions of her (D’Arcy was probably the best, saying earlier Madonna was “a very clear communicator and a good laugh”).

At the presser’s finale, another scrimmage of journos formed around Madonna to take photos of her on their cell phones — proving they’d been in the same room as a worldwide icon.