(A spokesman for Matteo Salvini, the leader of the anti-immigrant League, said the two would have liked to have met, but did not. A spokesman for the anti-establishment Five Star Movement, which won a third of Italian votes, did not return a request for comment.)

Aside from the occasional coffee at Campo de’ Fiori or photo-op at Piazza Navona, Mr. Bannon has been holed up in hotel rooms, taking meeting after meeting.

In Rome, he stayed at the luxurious Raphael hotel, where Bettino Craxi, the face of Italy’s corrupt establishment and mentor to Silvio Berlusconi, was pelted with coins in 1993 by an angry mob as he departed the political scene.

In Milan, he sat in a room at the grand Principe di Savoia, opposite a copy of Titian’s portrait of the Duke of Mantua, a master of intrigue in Renaissance Italy and a longtime sufferer of syphilis, surrounded by red damask wallpaper. Jams were on a room service cart, and a copy of a book titled “Headlines All My Life” was on the desk.

In both cities, he wore a blue and white striped button down over a polo shirt. In Rome the polo was orange. In Milan it was blue.

He sipped sparkling water and described a grand vision for a global populist future.

In the United States, Mr. Bannon said, he is working on a project to create a think tank to “weaponize” populist economic and social ideas.

He sees that work spreading to Europe, where a proliferation of populist websites in the image of Breitbart News, either owned by him or others, will spread those ideas, under his guidance.