 -- The U.S. Senate will delay its consideration of healthcare legislation while Sen. John McCain recuperates from surgery, Majority Leader Mitch McConnell announced Saturday night, just hours after the Arizona Republican announced he underwent a procedure to remove a blood clot from above his left eye.

"Elaine and I, along with the entire Senate family, wish John the very best and wish him a speedy recovery," McConnell said in a statement that referred to his wife, Transportation Secretary Elaine Chao. "While John is recovering, the Senate will continue our work on legislative items and nominations and will defer consideration of the Better Care Act."

McCain's absence from a procedural vote could have put the bill, which needs the support of 50 of 52 GOP senators to advance, in jeopardy. So far, Republican senators Susan Collins and Rand Paul have publicly stated they will not support a motion to proceed to floor debate on the legislation.

And McCain has expressed his displeasure with the bill. On Thursday he said in a statement, "The revised Senate health care bill released today does not include the measures I have been advocating for on behalf of the people of Arizona. That’s why if the Senate takes up this legislation, I intend to file amendments that would address the concerns raised by Arizona Governor Doug Ducey and other leaders across our state about the bill’s impact on Arizona’s Medicaid system."

McCain, 80, tweeted Saturday night, "Thanks to @MayoClinic for its excellent care –- I appreciate your support & look forward to getting back to work!"

Earlier in the evening, the Mayo Clinic announced in a statement that the surgery had taken place: "Following a routine annual physical, Sen. John McCain underwent a procedure to remove a blood clot from above his left eye on Friday, July 14 at Mayo Clinic Hospital in Phoenix," read the statement. "Surgeons successfully removed the 5-cm blood clot during a minimally invasive craniotomy with an eyebrow incision. Tissue pathology reports are pending within the next several days."

The statement continued, "The Senator is resting comfortably at home and is in good condition. His Mayo Clinic doctors report that the surgery went 'very well' and he is in good spirits. Once the pathology information is available, further care will be discussed between doctors and the family. In the meantime, his Mayo Clinic care team will not be conducting interviews."

And McCain's office acknowledged in a statement that he would remain in Arizona, writing, "Senator McCain received excellent treatment at Mayo Clinic Hospital in Phoenix, and appreciates the tremendous professionalism and care by its doctors and staff. He is in good spirits and recovering comfortably at home with his family. On the advice of his doctors, Senator McCain will be recovering in Arizona next week."

McCain's wife, Cindy McCain, retweeted her husband's statement, writing "A remarkable man!"

The McCains' daughter, Meghan McCain, tweeted, "Thank you to the incredible team at @mayoclinic Arizona for taking such good care of my father - he will be back soon."