Trump told reporters shortly after landing in Iraq he had flown in a "darkened plane with all windows closed, with no light anywhere; pitch black" to avoid it being tracked.
He also appeared to suggest that previous efforts to arrange a visit to a combat zone had been scrapped because of security concerns.
"We actually had a couple set up but were cancelled for security reasons because people were finding out," Trump said.
"Pretty sad when you spend $7 trillion in the Middle East and going in has to be under this massive cover with planes all over and all of the greatest equipment in the world and you do everything to get in safely."
Some have criticised the White House's security measures, suggesting they may need to use a more conspicuous aircraft in the future.
"Sources telling me Trump's on his way to visit troops - possibly in Iraq," Paul Rieckhoff, founder and chief executive of the advocacy group Iraq and Afghanistan Veterans of America, tweeted.
"Better late than never. But also a bit troubling that so many folks seem to already know about this if it hasn't happened already. #OpSec anyone?"
There were also other signs that Trump had left Washington.
The White House press office was unstaffed and did not issue any daily guidance for the president's schedule. The Marine who usually stands guard outside the West Wing when the president is in the White House also was nowhere to be seen.
Trump was also uncharacteristically absent from social media for 20 hours.
Trump eventually broke the silence after two posts on Christmas Day late Wednesday afternoon, with a tweet in which he shared a video of himself and first lady Melania Trump meeting troops in Iraq.
