The statement continues, "The Senator and his family are reviewing further treatment options with his Mayo Clinic care team. Treatment options may include a combination of chemotherapy and radiation."
McCain's doctors say he is recovering from surgery "amazingly well" and "his underlying health is excellent," according to the statement.
According to the American Brain Tumor Association, more than 12,000 people a year are diagnosed with glioblastoma. The American Cancer Society puts the five-year survival rate for patients over 55 at about 4 percent.
The David Farber Cancer Institute's Dr. David Reardon, one of the doctors who cared for the late Sen. Ted Kennedy, has confirmed to ABC News that Kennedy's tumor was also glioblastoma.
The 2008 Republican presidential nominee's medical history includes four melanomas removed during three separate surgeries in 1993, 2000 and 2002. It is possible for melanoma to spread to the brain, which could explain why doctors scanned him and discovered the clot that required last week's surgery.
"Senator McCain appreciates the outpouring of support he has received over the last few days," read the statement from McCain's office. "He is in good spirits as he continues to recover at home with his family in Arizona. He is grateful to the doctors and staff at Mayo Clinic for their outstanding care, and is confident that any future treatment will be effective. Further consultations with Senator McCain's Mayo Clinic care team will indicate when he will return to the United States Senate."
President Donald Trump said in a statement, "Senator John McCain has always been a fighter. Melania and I send our thoughts and prayers to Senator McCain, Cindy, and their entire family. Get well soon."
Cindy McCain posted on Instagram a photo from their wedding day, writing, "Thank you all for the wonderful thoughts. @SenJohnMcCain is doing well. We as a family will face the next hurdle together. One thing I know is he is the toughest person I know. He is my hero and I love him with all my heart."
Meghan McCain, the McCains' 32-year-old daughter tweeted, "The news of my father's illness has affected everyone one us in the McCain family."
ABC News' Mariam Khan and Dan Childs contributed to this report.