Giuliani, 81, came to global prominence in 2001 as he led New York's recovery from the September 11 attacks on the World Trade Center towers, which his spokesman said led to him developing 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 stabilise his condition," according to a statement, which added that Giuliani was now breathing on his own.
Giuliani remains in critical but stable condition at a Florida hospital and is being monitored as a precautionary measure, spokesman Ted Goodman said.
Giuliani's eight-year tenure as the mayor of the largest city in the United States was punctuated by the 9/11 attack just months before he left office.
He became celebrated as "America's mayor" for his leadership, knighted by Queen Elizabeth II and named Time magazine's Person of the Year.
Giuliani, a Republican, later made an unsuccessful run for president and was an adviser to US President Donald Trump, failing in a quest to overturn Trump's 2020 election defeat.
The 2020 effort led to criminal charges against Giuliani in two US states and a defamation lawsuit from election workers.
Giuliani has denied wrongdoing in the criminal cases.
New York's current mayor Zohran Mamdani, a Democrat, on Monday wished Giuliani a steady recovery.
"He's been a fixture in our city's politics and public life for so many years. And I know that many New Yorkers are concerned by the reports that he's in critical condition," Mamdani said.
with AP
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