WASHINGTON, United States (AFP) — Flags were flying at half-staff yesterday over the White House and US Capitol in honour of John McCain, the Vietnam War hero and two-time presidential candidate with a legendary temper whose personal courage and insistence on treating even his foes with respect earned him near-universal admiration.

McCain died on Saturday, four days shy of his 82nd birthday, following a year-long battle with an aggressive form of brain cancer. He is survived by his wife Cindy and seven children, three of them by an earlier marriage.

Senate leaders of both parties announced that McCain will lie in state in the US Capitol Rotunda, without specifying the timing.

That honour has been accorded to only a few notable Americans, including John F Kennedy, Ronald Reagan and civil rights icon Rosa Parks.

Senate Republican Majority Leader Mitch McConnell called McCain “a great American patriot”.

Arizona Governor Doug Ducey confirmed on Twitter that McCain will also lie in state at the Capitol building in Phoenix on Wednesday, McCain’s birthday. “This is a rare and distinct occurrence for a truly special man,” he said, adding: “John McCain is Arizona.”

In Phoenix, a succession of ordinary Arizonans left flags or flowers at McCain’s office or a local mortuary to honour the man who represented them in Congress for 35 years.

His funeral is expected to take place in the massive National Cathedral overlooking Washington before he is laid to rest, according to his wishes, at the Naval Academy in nearby Annapolis, Maryland.

Former presidents George W Bush, a Republican, and Barack Obama, a Democrat — his successful rivals in, respectively, the 2000 and 2008 elections — are set to speak at the funeral, according to The New York Times.

Media reports earlier this year said the senator had expressly asked that President Donald Trump not be invited. Instead, Vice-President Mike Pence is expected to attend.

As tributes poured in from the US and abroad, Trump said simply that he sent his “deepest sympathies and respect” to the McCain family.

A rare Republican critic of Trump, McCain had accused the president of “naivete”, “egotism” and of sympathising with autocrats, especially after Trump’s widely criticised appearance in Helsinki alongside Russian President Vladimir Putin.

McCain cast a decisive vote last year that killed Republican attempts to repeal Obama’s health care reforms. The repeal was a Trump priority, and the president never forgave McCain.

The hawkish McCain was an unrelenting critic of Obama’s foreign policy, saying the Democratic president was weak on Libya, Iraq and Syria.

Still, Obama said he and the senator “shared, for all our differences, a fidelity to something higher — the ideals for which generations of Americans and immigrants alike have fought, marched and sacrificed”.

Bush, whose tough campaign against McCain in 2000 left both sides bruised, praised the Arizonan as “a man of deep conviction and a patriot of the highest order”.

Ordinary Americans also paid tribute, many of them in Phoenix, McCain’s hometown.

“I didn’t agree with him all the time,” said Michelle Hasnelle of Phoenix, “(but) he was always for the people of Arizona — he was one of us.”

McCain spent more than three decades in the Senate, looming large in debates over war and peace and the moral direction of the nation.

As chairman of the Senate Armed Services Committee, he was a powerful advocate for the nation’s veterans.

As a fervent Atlanticist, a persistent critic of authoritarian leaders, and a frequent congressional traveller, he earned respect around the globe.

German Chancellor Angela Merkel called McCain “one of the great political figures of our time (who) fought tirelessly for a strong transatlantic alliance”.

Canadian Prime Minister Justin Trudeau said he was “an inspiration to millions”. McCain “embodied the idea of service over self”, according to British Prime Minister Theresa May, while French President Emmanuel Macron saluted “a true American hero”.

Across the Pacific, the China Daily referred to him as a “titan of American politics”.

Sarah Palin, whom McCain plucked from obscurity to become his 2008 White House running mate, described him as “a fighter, never afraid to stand for his beliefs”.

McCain drew criticism from the left for giving a platform to Palin’s right-wing views, which contributed to the rise of the conservative Tea Party movement.

But he also earned respect from liberals for his steadfast opposition to torture and his push for immigration reform.

Top Senate Democrat Chuck Schumer said he would seek to rename a Senate building in his honour.

Praise for McCain, however, was not universal: Chinese social media users called him an “enemy of China” for his hawkish foreign policy views.

And comments on the US far-right Breitbart website slammed the senator for his key vote against the Obamacare repeal.

McCain had been away from the Senate floor since December, remaining at his Arizona ranch for treatment of glioblastoma — the same form of brain cancer that took the life of another Senate giant, Democrat Ted Kennedy, in 2009.

The son and grandson of four-star admirals, McCain will be buried in the cemetery of the US Naval Academy in Annapolis, on a peaceful hillside overlooking the Severn River.

As a student at the academy, he had a reputation as a rebel, but with a wit and charm that drew people to him.

In 2015, McCain himself revealed the simple epitaph he wanted on his tombstone, which will stand alongside those of naval heroes going back to the 1800s: “He served his country”.