Six-term Sen. John McCain of Arizona, the influential Republican who has clashed with presidents of both parties over national security and foreign policy, has been diagnosed with brain cancer, his office said in a statement Wednesday night.

The cancer was discovered after minor surgery last week to remove a blood clot above the left eye of the 80-year-old chairman of the Senate Armed Services Committee and 2008 Republican presidential nominee, according to the Mayo Clinic.

“Subsequent tissue pathology revealed that a primary brain tumor known as a glioblastoma was associated with the blood clot,” the Phoenix clinic said in a statement. “The senator and his family are reviewing further treatment options with the Mayo Clinic care team. Treatment options may include a combination of chemotherapy and radiation.”

Glioblastoma is an aggressive form of cancer, the same kind that killed vice presidential son Beau Biden. According to the American Cancer Society, for people older than 55, the five-year survival rate for glioblastoma is about 4 percent.

Mr. McCain’s office said the question of his return to the Senate will be determined after further consultations with his medical team.

CNN, citing medical sources involved with Mr. McCain’s treatment, reported that he showed no neurological problems before or after the more than three-hour surgery to remove the tumor.

The news stunned official Washington on both ends of Pennsylvania Avenue.

President 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.”

Vice President Mike Pence said he and his wife, Karen, were praying for Mr. McCain. “Cancer picked on the wrong guy,” Mr. Pence tweeted.

Senate Majority Leader Mitch McConnell, Kentucky Republican, called Mr. McCain a Vietnam War POW, a “hero to our country,” and said his colleagues hope for his return to the Senate soon.

“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,” Mr. McConnell said in a statement. “The entire Senate family’s prayers are with John, Cindy and his family, his staff, and the people of Arizona he represents so well. We all look forward to seeing this American hero again soon.”

Mr. McCain’s office said he “appreciates the outpouring of support he has received over the last few days. He is in good spirits as he continues to recover at home with his family in Arizona.”

The senator’s daughter Meghan noted that her father, a prisoner in North Vietnam for five years, has battled cancer previously and asked for the nation’s prayers.

In 2000, he underwent surgery to remove melanoma, though reports at the time and during his 2008 presidential bid said the skin cancer did not seem to have spread.

Miss McCain said her father is “confident and calm” about his latest health challenge.

“He is the toughest person I know,” she said. “The cruelest enemy could not break them. The aggressions of political life could not bend him. So he is meeting this challenge as he has every other.”

Mr. McCain fractured both arms and a leg ejecting from his aircraft over North Vietnam and was held for more than five years in Hanoi’s main Hoa Lo Prison, which was nicknamed the “Hanoi Hilton.” To this day, Mr. McCain cannot raise his hands over his head to comb his hair.

“Cancer may afflict him in many ways. But it will not make him surrender,” Miss McCain said in a heartfelt post. “Nothing ever has. He is a warrior at dusk, one of the greatest Americans of our age.”

Former President Barack Obama, who defeated Mr. McCain in the 2008 presidential contest, praised the senator on Twitter on Wednesday night.

“John McCain is an American hero & one of the bravest fighters I’ve ever known,” Mr. Obama said. “Cancer doesn’t know what it’s up against. Give it hell, John.”

Other Democrats to post support on social media included former President Bill Clinton, 2016 presidential nominee Hillary Clinton and House Minority Leader Nancy Pelosi.

Sen. Ben Sasse, Nebraska Republican, called Mr. McCain “an American hero and a relentless fighter.”

“I wish him Godspeed in this fight and look fwd to welcoming him back to work soon,” Mr. Sasse said on Twitter.

Mr. McCain’s 2008 running mate, former Alaska Gov. Sarah Palin, said on Facebook, “John McCain is one tough fighter — we know he’ll face this diagnosis with courage and strength. Our family continues to lift John and his family up in prayer.”

Sen. Johnny Isakson, Georgia Republican, called his colleague “one of the greatest Americans of my generation.”

“He, Cindy and the entire McCain family are in my prayers. God bless John McCain,” Mr. Isakson said.

Sen. Claire McCaskill, Missouri Democrat and a cancer survivor, told Mr. McCain on Twitter, “Hey John! We can’t wait to welcome you to the club. You got this!”

Sen. Angus King, Maine independent, tweeted, “I love John McCain. I’ve traveled with him, I’ve been tongue lashed by him, I’ve worked with him, and I wish I could be with him tonight.”

House Speaker Paul D. Ryan, Wisconsin Republican, said Mr. McCain “has always been a warrior.”

“It’s who he is. I know John is going to fight this with the same sheer force of will that has earned him the admiration of the nation,” Mr. Ryan said. “And all of us, not as Republicans or Democrats, but as Americans, are behind him. The prayers of the whole House are with Senator McCain and his family.”

The blood clot was the latest health challenge for Mr. McCain, though the Mayo Clinic said his overall health is fine and he is “recovering from his surgery amazingly well.”

His absence from the Senate forced a delay in the vote on a health care bill on which Republicans could not afford to have any member be absent. Mr. McConnell later pulled the bill anyway when several other Republicans announced that they would vote against it.

On Monday, before the cancer diagnosis, Mr. Trump wished Mr. McCain a speedy recovery, joking that Republicans needed his vote on the health care legislation.

• Victor Morton and Seth McLaughlin contributed to this report.

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