The update came after officials said that Giuliani was hospitalized in critical condition on Sunday.
Spokesman Ted Goodman said that on 9/11, Giuliani "ran toward the towers to help those in need, which later led to a diagnosis of restrictive airway disease."
"This condition adds complications to any respiratory illness, and the virus quickly overwhelmed his body, requiring mechanical ventilation to maintain adequate oxygen and stabilize his condition," Goodman said.
Goodman said that Giuliani is now breathing on his own, with his family and primary medical provider at his side.
"Mayor Giuliani is the ultimate fighter, as he has demonstrated throughout his life, and he is winning this battle," Goodman said. "His family deeply appreciates the outpouring of love and support. The mayor believes in the power of prayer, and we are feeling that strength today."
He remains in critical but stable condition.