The late senator John McCain has taken a final swipe at longtime foe US President Donald Trump in a posthumous message to the American people.

The message, conveyed by a McCain family spokesman on Tuesday morning comes as the White House has been accused of disrespect for not properly honouring the veteran lawmaker.

Mr McCain died of brain cancer at the age of 81 on Sunday (AEST). The US senator and Vietnam veteran had traded barbs with Mr trump on numerous occasions in what was a long-running feud.

Rick Davis, a McCain family friend, read out the posthumous message from Mr McCain, in which the late senator appeared to take a thinly veiled dig at Mr Trump.

In the message, McCain urged Americans not to “hide behind walls”.

The American people are “a nation of ideals, not blood and soil,” Mr Davis said as he read from McCain’s letter at the Arizona State Capitol building in Phoenix.

“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,” he said.

“We weaken it when he hide behind walls rather than tear them down.”

In his posthumous letter, Mr McCain also told his fellow Americans not to “despair of our present difficulties”.

Mr Davis confirmed that former presidents George W Bush and Barack Obama will pay tribute to Mr McCain at his funeral ceremony at Washington’s National Cathedral, but Mr Trump would not attend.

“The President will not be, as far as we know, attending the funeral,” Mr Davis said. “That’s just a fact.”

Later, the White House buckled under bi-partisan pressure by returning its US flags to half-mast.

Mr Trump had ordered the flags to fly at half-mast on Saturday evening after Mr McCain’s death, but by Monday they were back to normal.

Flags at the US Capitol and other Washington federal landmarks remained at half-mast.

Leading Democrat Chuck Schumer and Republican counterpart Mitch McConnell said flags on all government buildings should remain at half-mast until Mr McCain’s burial.

Some defended the White House, saying it was following the established procedure by lowering its flags “on the day of death and the following day for a Member of Congress”.

Others, however, pointed out that tradition dictates that flags should remain lowered to honour lawmakers and major public figures until their funerals.

“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,” Mr Trump said in a statement issued by the White House on Tuesday morning.

After Democratic Senator Ted Kennedy died in 2009, then-president Barack Obama ordered flags at the White House be flown at half-mast for five days.

Mr Trump had the White House flags lowered this year from when former first lady Barbara Bush died until her funeral.

New York Governor Andrew Cuomo was unequivocal in blaming Mr Trump for the perceived snub, saying on Twitter: “Senator McCain was twice the public elected official Donald Trump will ever be.”

New York government flags remained at half-mast Tuesday.

Mr McCain’s body will lie in state at the Arizona State Capitol on Wednesday local time, and at the US Capitol Rotunda in Washington on Friday.

-with agencies