Rudy Giuliani is showing clear signs of improvement after a serious bout of pneumonia left him in critical condition, with his son Andrew Giuliani saying Tuesday that the former New York City mayor is now awake, breathing on his own, and even in good spirits.

“Good news update: Thank you for the love and support you’ve shown my Dad over the past few days,” the younger Giuliani said.

“Just yesterday he was in critical condition, so I’m incredibly grateful to share that he is now conscious, off the ventilator, and even cracking jokes.”

Giuliani, 81, was admitted to the hospital over the weekend after developing pneumonia, which was reportedly worsened by a respiratory condition linked to his exposure during the September 11, 2001 terror attacks.

According to those close to him, he had lapsed into a coma but regained consciousness on Monday.

Tom Von Essen, a longtime friend who served as New York City fire commissioner during 9/11, said Tuesday morning that Giuliani’s condition appears to be improving.

“It looks like Rudy’s has turned a corner. We hope he continues to improve,” said Von Essen, who has been briefed on his condition.

“I worry about him. What he has done for New York City and the compassion he showed 9/11 families is remarkable. I hope he has a great recovery.”