McCain had spent several days last week at Walter Reed National Military Medical Center in Bethesda, Maryland recovering from side effects stemming from chemotherapy treatment for brain cancer.
His daughter Meghan said her father would be spending the holidays in Arizona.
In a brief statement, the senator's office provided an assessment from Mark Gilbert, chief of neuro-oncology at the National Institutes of Health's National Cancer Institute.
President Donald Trump on Friday telephoned Cindy McCain, the wife of ailing Sen. John McCain (R-Ariz.) would return to Washington if his vote was needed to pass the tax overhaul bill. He added: "But the word is John will come back if we need his vote. But he will come back if we need his vote".
If the count is deadlocked, Vice President Mike Pence would cast the tie-breaking vote in favor of Republicans.
After his summer surgery, McCain rebounded quickly, returning to Washington and entering the Senate on July 25 to a standing ovation from his colleagues.More news: U.S. vetoes United Nations vote on status of al-Quds
"He is grateful for the excellent care he continues to receive, and appreciates the outpouring of support from people all over the country", the statement said.
The House and Senate are scheduled to vote this week on Trump's top legislative accomplishment, a sweeping tax package.
Thank you to everyone for their kind words.
McCain in July was diagnosed with glioblastoma, a deadly form of brain cancer, which was revealed after he underwent a surprise emergency July 14 craniotomy to remove a blood clot above his left eye. The final vote on the Republican tax bill is slated for sometime this week. Marco Rubio (R-FL) and Bob Corker (R-TN) announced their support for the bill after winning some amendments or provisions.
Meghan McCain's new husband, The Federalist's Ben Domenech gave an update on the senator's condition after the longtime Arizona senator was hospitalized earlier this week.
McCain, 81, was admitted to the hospital for what is office called "normal side effects" of his cancer treatment last week.