McCain will undergo physical therapy and rehabilitation at the Mayor Clinic in Arizona.
"He is grateful for the excellent care he continues to receive, and appreciates the outpouring of support from people all over the country". He will not be present for the final vote on the GOP tax bill expected early this week, the report added.
The Senate already passed the tax bill once, but must do so again now that it has been joined with the House's version.
John McCain has returned home to Arizona to spend Christmas with his family.
Sen. McCain announced in July that he had a glioblastoma, an aggressive brain tumor, after doctor's discovered it while removing of a blood clot.
He left for Arizona on Sunday.
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Republican Sen. John McCain has returned home to Arizona, where he plans to stay until January, after he was hospitalized over side effects from treatment of brain cancer, the senator's office announced Sunday. He has been undergoing treatment since. They still hold a 52-48 majority, and given Vice President Mike Pence's tie breaker, they can afford to lose two Republican votes - from either absence or opposition - and still be able to pass the bill.
No Democrats or independents support the legislation, although it is expected to comfortably pass the House of Representatives.
President Donald Trump told reporters Sunday he had spoken to Cindy McCain.
He said: "But the word is that John will come back if we need his vote".
The 81-year-old senator is responding positively to treatment, according to the senator's daughter, Meghan McCain. "And it's too bad, he's going through a very tough time, no question about it, but he will come back if we need his vote". Marco Rubio of Florida and Bob Corker of Tennessee last week and should have enough votes for the GOP measure. "They've headed back [to Arizona]", Trump said. McCain eventually began using a wheelchair, with members of his staff pushing him where he needed to go.