The White House didn't immediately respond to questions Monday.
This move breaks with tradition in which the White House flags are generally flown at half-mast until the burial of a lawmaker and other notable personalities, and is done so in order to honor such figures.
Tributes have been paid in Vietnam to John McCain, the American senator and former navy pilot shot down over Hanoi during the United States war with the southeast Asian nation.
The Arizona Republican, whose relationship with President Trump has always been fraught, died on Saturday at the age of 81 after battling brain cancer.
Karen Travers tweeted "Flags at the White House were lowered to half staff this weekend for the passing of John McCain but this morning they are back to full staff".
Some said the White House was simply following proper procedure because US Flag Code states that flags be lowered "on the day of death and the following day for a Member of Congress".
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And Mr Trump himself issued flag flying proclamations following mass shootings in Las Vegas and Parkland, Florida.
The flags at the White House had been lowered a day earlier. Trump tweeted condolences to McCain's family but made no reference to the Arizona senator.
The contrast offered the latest reminder of the animosity that Trump has maintained for McCain, even after his passing. While on the campaign trail in 2015, then-candidate Trump suggested McCain was not a war hero because he had been captured in Vietnam.
President George W. Bush was the first to make common practice lowering the staff for natural disasters, and President Barack Obama lowered the flag more than any other President. "Our hearts and prayers are with you!"
McCain died on Saturday at 81 after a 13-month struggle with brain cancer. Vice President Mike Pence has also been invited to the funeral.
He will be buried in a private service at the US Naval Academy at Annapolis, where his service to his country began six decades ago, at a cemetery overlooking Maryland's Severn River. A formal ceremony will take place in the Rotunda at approximately 11 a.m., on Friday, honoring Senator McCain's life and service to the nation.