President Donald Trump pushed back against claims that the White House or his campaign brought and distributed his signature "Make America Great Again" hats to US troops when he visited Iraq on Christmas.

Some of the troops were seen with the hats and at least one Trump flag as they waited for the president.

In a statement to Business Insider, the Air Force denied that the hats had been distributed at Ramstein Air Base, Germany, and said they were "personal items."

Although service members are encouraged to "to carry out the obligations of citizenship," regulations "prohibits the wearing of a military uniform during or in connection with the furtherance of any political or commercial interests."

While some veterans on social media accused the service members of engaging in partisan political activities while in uniform, the event may have blurred what is normally a clear distinction between a partisan activity and a purported candid visit from their commander-in-chief.

President Donald Trump pushed back against claims that the White House brought and distributed his signature "Make America Great Again" campaign hats to US troops when he visited Iraq and Germany on Christmas Day.

Trump accused some news outlets, namely CNN, of making that assertion.

"If these brave young people ask me to sign their hat, I will sign. Can you imagine my saying no?" the president asked, saying that his team did not distribute any hats.

It was unclear whether CNN reported the hats were distributed by Trump's team on the ground; however, a CNN article updated several hours before Trump's tweet included several denials from press secretary Sarah Huckabee Sanders and military officials.

The controversy stems from the numerous photos and reports of Trump signing campaign memorabilia for troops in Iraq and Germany. Trump, who was widely criticized for not visiting US troops on or before Christmas, dispelled the notion with his surprise trip with the first lady and senior staffers.

Watch: Meet the woman behind Trump's $20 million merch empire

Trump received some criticism after he was pictured signing the campaign memorabilia, leading some to believe he or his campaign handed out the items for a photo-op. Some of the troops, both officers and non-commissioned officers alike, were seen with hats and at least one Trump flag as they waited for the president to arrive at a aircraft hangar.

One Air Force captain who held a Trump flag was reportedly ordered to put it aside by an official, but took it back out after the president arrived, according to Stars and Stripes.

In a statement to Business Insider, the Air Force denied that the items were pre-distributed at Ramstein Air Base, Germany, where Trump stopped on his way back to the US: "Photos of the event show personal items; materials were not given to Airmen by the White House."

US Air Forces Europe said the personal items did not violate the military's rules: "There is no rule against Airmen bringing personal items to be signed by the president," a statement from USAFE said, according to the Military Times.

Press secretary Sanders also confirmed to CNN that the hats pictured in Iraq were personal goods brought by the service members.

Service members are encouraged to "to carry out the obligations of citizenship," which could include joining a partisan political club or making monetary contributions to political groups, but military regulations "prohibits the wearing of a military uniform during or in connection with the furtherance of any political or commercial interests."

US Army Spc. Jesse Thorsen speaks at a campaign rally in support of Republican presidential candidate Ron Paul. Office of Under Secretary of Defense for Personnel & Readiness via Reuters

The latest incident stands in contrast to that of Spc. Jesse Thorsen, a US Army Reservist who wore his combat uniform and endorsed then-Republican presidential candidate Ron Paul at a campaign rally in 2012.

Thorsen, who was later reprimanded by the Army, defended his actions and said if "the Army works for Congress ... if a Congressman invites you up on stage, doesn't he have the right to do that?"

But Trump's other actions during his visit attracted criticism and resurfaced the allegation that he seeks to politicize what is supposed to be an apolitical military.

During his Christmas Day visits with the troops, Trump revisited his typical rhetoric.

"The United States cannot continue to be the policeman of the world," Trump said to a crowd of troops in al-Asad Air Base, Iraq. "It's not fair when the burden is all on us, the United States."

Trump also peddled his repeated claim that US service members received a pay raise for the first time "in more than 10 years" — despite the fact that troops have been receiving a pay raise every year for over 30 years.