The malignant tumour was discovered last week during his surgery to remove a blood clot from above his left eye.

McCain is a six-term senator and the 2008 Republican Presidential candidate.

He underwent surgery on Friday at a facility in Phoenix, Arizona.

"The senator's doctors say he is recovering from his surgery 'amazingly well' and his underlying health is excellent," a statement from the clinic read.

"Treatment options may include a combination of chemotherapy and radiation," it added.

Calling him a 'fighter', US President Donald Trump tweeted: "Melania and I send our thoughts and prayers to Senator McCain, Cindy, and their entire family. Get well soon."

Former President Barack Obama hailed McCain as a hero.

"John McCain is an American hero & one of the bravest fighters I've ever known. Cancer doesn't know what it's up against. Give it hell, John," his tweet read.

McCain's daughter in a statement posted on Twitter said that the senator reacted in a calm and confident manner upon learning about his disease.

The Arizona senator is a Vietnam veteran and spent more than five years as a prisoner of war (POW).

Image: twitter.com/SenJohnMcCain