An order to have a ship named for the late Senator John McCain hidden from view during Donald Trump’s recent visit to Japan was “not an unreasonable thing to ask”, the president’s chief of staff said on Sunday.

Mick Mulvaney made the startling claim even as it was reported that the Pentagon has told the White House to stop politicizing the military.

The US navy has confirmed reports about an internal email that said the White House military office wanted the USS John McCain kept “out of sight” when Trump was in Japan. The email was first reported by the Wall Street Journal.

McCain died last year at 81, from brain cancer. The 2008 Republican presidential nominee remained fiercely at odds with Trump over his military service in Vietnam and Trump’s absence from that war, and over political matters including a healthcare overhaul that sunk on his vote in the Senate. Since McCain’s death, Trump has continued his attacks.

Trump said this week he knew nothing about the request to hide the ship named after McCain. But he also said: “Somebody did it because they thought I didn’t like him, OK? And they were well-meaning, I will say.”

On Sunday, Mulvaney told NBC’s Meet the Press: “The fact some 23- or 24-year-old person went to that site and said, ‘Oh my goodness, there’s the John McCain, we all know how the president feels about the former senator, that’s not the best backdrop, can somebody look into moving it?’

“That’s not an unreasonable thing to ask.”

Press interest in the story, Mulvaney claimed, was “outrageous”.

In South Korea, the acting defense secretary, Patrick Shanahan, told reporters he was not planning to seek an investigation by the Pentagon’s internal watchdog, “because there was nothing carried out” by the navy. But he also said he needed to gather more information about what happened.

“How did the people receiving the information – how did they treat it,” Shanahan said. “That would give me an understanding on the next steps.”

Mulvaney said it would be “silly” if anyone was fired over the email.

“The president’s feeling towards the former senator are well known,” he said. “They are well known throughout the office, they are well known in the media.”

Shanahan also said he had spoken to McCain’s wife, Cindy, though he did not reveal what was said. McCain’s daughter Meghan, a television pundit, said this week: “It’s impossible to go through the grief process when my father, who’s been dead 10 months, is constantly in the news cycle because the president is so obsessed with the fact that he’s never going to be a great man like he was.”

The McCain incident has dogged Shanahan through his trip to Asia, in which he has tried to deal with national security issues involving China and North Korea. Shanahan is yet to be formally nominated. The McCain issue is sure to come up at any Senate confirmation hearing.

A spokesman for Shanahan, Lt Col Joseph Buccino, told the Associated Press the secretary told his chief of staff on Friday to speak to the White House military office “and reaffirm his mandate that the Department of Defense will not be politicized”.

Shanahan told reporters he was told that despite the White House request, the navy did not move the USS John McCain and that a barge in front of it was moved before Trump arrived to visit the USS Wasp. He said a tarpaulin that had been draped over the ship’s name was removed, having been put there for maintenance reasons only.

Asked if his senior staff were aware of the White House request, Shanahan said he had been told they were not. He has also said he was not aware of the request and would not have authorized it.

It is not known who at the Pentagon may have known about the request to hide the USS John McCain. It is also not clear whether navy leaders deliberately chose its crew to be on leave during Trump’s visit, or if other measures were taken to ensure that the ship was not visible from where the president stood on the Wasp.

The warship was commissioned in 1994 and named for the senator’s father and grandfather, both navy admirals named John Sidney McCain. Last year, the navy rededicated the ship to honor the senator too.