Former New York City Mayor Rudy Giuliani remained hospitalized Monday with pneumonia — with a longtime friend telling The Post, “Today is an important day.”

The 81-year-old’s shocking weekend hospitalization occurred after he came down with pneumonia, said Giuliani’s business partner Tom von Essen, who served as the city’s fire commissioner during 9/11.

“Rudy had a tough weekend. He had pneumonia,” von Essen said.

“Today is an important day,” he said.

A spokesman for Giuliani said Sunday that the close ally of President Trump was in critical but stable condition with a publicly undisclosed ailment, prompting widespread concern and well wishes for his health.

Von Essen repeated that Giuliani’s condition remained stable Monday morning.

“He seems to be doing OK,” added Giuliani spokesman Ted Goodman.