U.S. Senator John McCain has been diagnosed with a brain tumor after doctors removed a blood clot above his left eye last week, his office said in a statement Wednesday.

The 80-year-old Republican has glioblastoma, an aggressive cancer, according to doctors at the Mayo Clinic in Phoenix. The Arizona senator and his family are reviewing further treatment, including a combination of chemotherapy and radiation.

"On Friday, July 14, Senator John McCain underwent a procedure to remove a blood clot from above his left eye at Mayo Clinic Hospital in Phoenix. Subsequent tissue pathology revealed that a primary brain tumor known as a glioblastoma was associated with the blood clot," his office said in a statement.

About 20,000 people in the U.S. each year are diagnosed with a glioblastoma, a particularly aggressive type of brain tumour. The American Cancer Society puts the five-year survival rate for patients over 55 at about 4 per cent.

The tumour digs tentacle-like roots into normal brain tissue. Patients fare best when surgeons can cut out all the visible tumour, which happened with McCain's tumour, according to his office.

That isn't a cure; cancerous cells that aren't visible still tend to lurk, the reason McCain's doctors are considering further treatment including chemotherapy and radiation.

The senator and chairman of the Armed Services Committee had been recovering at his Arizona home. His absence had forced majority leader Mitch McConnell, Republican from Kentucky, to delay action on health care legislation.

In a statement, McConnell said: "John McCain is a hero to our Conference and a hero to our country. He has never shied from a fight and I know that he will face this challenge with the same extraordinary courage that has characterized his life. The entire Senate family's prayers are with John, Cindy and his family, his staff, and the people of Arizona he represents so well."

Doctors say McCain is recovering from his surgery amazingly well and his underlying health is excellent, according to the statement.

His office disclosed the removal of the blood clot late Saturday and said the senator was awaiting pathology reports. In the past, McCain had been treated for melanoma.

In a statement on Twitter, his daughter, Meghan McCain, said: "My love for my father is boundless and like any daughter I cannot and do not wish to be in a world without him. I have faith that those days remain far away."

With his irascible grin and fighter-pilot moxie, McCain was elected to the Senate from Arizona six times, but twice thwarted in seeking the presidency.

An upstart presidential bid in 2000 didn't last long. Eight years later, he fought back from the brink of defeat to win the Republican nomination, only to be overpowered by Barack Obama. McCain chose a little-known Alaska governor as his running mate in that race, and helped turn Sarah Palin into a national political figure.

After losing to Obama in an electoral landslide, McCain returned to the Senate, determined not to be defined by a failed presidential campaign. And when Republicans took control of the Senate in 2015, McCain embraced his new job as chairman of the powerful Armed Services Committee, eager to play a big role "in defeating the forces of radical Islam that want to destroy America."

Throughout his long tenure in Congress, McCain has played his role with trademark verve, at one hearing dismissing a protester by calling out, "Get out of here, you low-life scum."

McCain stuck by the party's 2016 presidential nominee, Donald Trump, at times seemingly through gritted teeth — until the release a month before the election of a lewd audio in which Trump said he could kiss and grab women. Declaring that the breaking point, McCain withdrew his support and said he would write in "some good conservative Republican who's qualified to be president."

He had largely held his tongue earlier in the campaign when Trump questioned his status as a war hero.

McCain said that was offensive to veterans, but "the best thing to do is put it behind us and move forward."

On Wednesday, Trump said in a statement that McCain "has always been a fighter."

The president said he and wife, Melania, "send our thoughts and prayers to Senator McCain, Cindy, and their entire family," adding, "Get well soon."​

He also received well-wishes from former president George H.W. Bush, who released a statement saying: "The Hanoi Hilton couldn't break John McCain many years ago, so Barbara and I know — with confidence — he and his family will meet this latest battle in his singular life of service with courage and determination."

Politics aside, McCain and Bill Clinton developed a strong friendship, and the former president said: "As he's shown his entire life, don't bet against John McCain. Best wishes to him for a swift recovery."

Former vice-president Joe Biden and Democratic Senator Bernie Sanders tweeted about McCain's health, calling him "strong" and a "hero" respectively.