The Pentagon has warned the White House not to politicise the military, amid a row over a ship bearing the same name as late Senator John McCain.
Last week, the White House asked for the USS John S McCain to be hidden during his speech in Japan.
McCain, who died last year, was a fierce critic of President Trump.
The plans were never implemented and acting Pentagon chief Patrick Shanahan says he will not escalate an inquiry into the incident.
"There is no room for politicising the military," Mr Shanahan told reporters. "I'll deal with this in an appropriate manner."
Mr Shanahan's spokesman, Lt-Col Joe Buccino, also said that the Pentagon had raised the issue with the White House at a meeting on Friday.
White House chief of staff Mick Mulvaney told US broadcaster NBC that the request to move the ship was likely to have been made by someone on the president's team.
But, he said, it was "not an unreasonable thing to ask" and that no-one would be fired over the request.
President Trump defended the request last week, saying that while he was unaware of that it had been made, the person behind it was "well meaning" in their intention.
He added that he "couldn't care less" that the warship bears the name of John McCain, who was a military veteran and Republican senator for Arizona.
During the Vietnam war, Senator McCain was imprisoned and tortured for five-and-a-half years.
His outspoken criticism of Mr Trump during the presidential election campaign in 2015 sparked a bitter rivalry between the two that continued until his death in August last year - and even beyond.