Flags at some federal buildings were fully raised on Monday, far earlier than would normally be expected after such an event.
Mr Trump tweeted his condolences to the McCain family, but has not offered a tribute to the veteran's life.
The pair had a fractious relationship.
Mr Trump appeared to repeatedly ignore media questions about the flag before announcing that it would be lowered again.
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."
He also confirmed reports he will not attend McCain's funeral next weekend.
The statement said other members of the Trump administration, includin
g his chief of staff and secretary of defence, will attend instead.
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