McCain has expressed concern about the health care bill, but has not said how he would vote.
"While John is recovering, the Senate will continue our work on legislative items and nominations, and will defer consideration of the Better Care Act", said Senate Majority Leader Mitch McConnell in a written statement.
An analysis and score of the Senate GOP's new healthcare bill from the Congressional Budget Office is expected on Monday.
With McCain away, unless one of those two senators changes their mind, Senate Republican leaders are unlikely to meet the 50-vote threshold needed to begin debate on the bill. He will be in Arizona next week as he recovers based on the advice of his doctors, the statement said. Vice President Mike Pence would break a tie for final passage.
N Korea warns of nuclear 'tipping point' over U.S. bomber drill
The complaints, made in unusually strident language, follow a phone conversation between President Xi Jinping and U.S. But opinion is more divided in the developing countries in the region.
"Following a routine annual physical, Sen". McCain was reported to be resting comfortably at his home in Arizona.
Mayo Clinic Hospital doctors said Saturday that McCain underwent a "minimally invasive" procedure to remove the almost 2-inch (5-centimeter) clot, and that the surgery went "very well".
"Surgeons successfully removed the 5-cm blood clot during a minimally invasive craniotomy with an eyebrow incision", Mayo Clinic said in a statement.
Two Republican senators - Rand Paul of Kentucky and Susan Collins of ME - have already announced opposition to proceeding to the most version of the health care reconciliation bill. 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".