Earlier this month, when he signed a multi-billion dollar defence bill named after McCain, the president did not say his name.

It urged the nation not to "hide behind walls" and said the American people are "a nation of ideals, not blood and soil".

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Senior Democrat Chuck Schumer and top Republican Mitch McConnell said the flags on all government buildings should be at half-staff for the late senator until his burial next Sunday.

On Monday night, Mr Trump spoke about McCain during a dinner for evangelical leaders, saying "our hearts and prayers" are going to the late senator's family "and we very much appreciate everything that Senator McCain has done for our country".

But on Monday afternoon, he said in a statement: "Despite our differences on policy and politics, I respect Senator John McCain's service to our country and, in his honour, have signed a proclamation to fly the flag of the United States at half-staff until the day of his interment."

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Flags at the US Capitol and other Washington landmarks remained at half-staff earlier on Monday, but the White House had returned to its usual levels.

McCain also told his country folk: "Do not despair of our present difficulties, but believe always in the promise and greatness of America".

US President Donald Trump has announced the White House flag will be returned to half-staff, after critics attacked his response to the death of Republican senator John McCain.

The White House was urged by senators of both parties to honour that protocol, and critics asked why a proclamation had not been issued as it was after the deaths of other political figures, such as former First Lady Barbara Bush.

Flags at some federal buildings were fully raised on Monday, earlier than would normally be expected after such an event.

Former Presidents George W Bush and Barack Obama will pay tribute to McCain during his funeral ceremony on Saturday at the National Cathedral.

Earlier on Monday, before the flag U-turn, McCain family friend Rick Davis read out a posthumous message prepared by the senator before his death from brain cancer on Saturday.

"We weaken our greatness when we confuse our patriotism with tribal rivalries that have sown resentment and hatred and violence in all the corners of the globe," McCain had said.

Mr McCain's body will lie in state in the Arizona State Capitol on Wednesday and at the US Capitol Rotunda on Friday, giving his colleagues and the public a chance to pay their respects.

Some said the White House was simply following proper procedure, however, because US Flag Code states that flags be lowered "on the day of death and the following day for a Member of Congress".