A protestor has been arrested near the White House after setting fire to an American flag to demonstrate against President Donald Trump's executive order targeting such acts, police said.

The arrest on Monday evening came hours after Trump signed an order directing the Justice Department to pursue legal action against flag-burners, despite Supreme Court rulings that say burning of US flags is constitutionally protected.

"I'm burning this flag as a protest to that illegal fascist president that sits in that house," the man shouted into a bullhorn in Lafayette Park, adjacent to the White House, according to video shared on social and local media.

Claiming to be a 20-year combat veteran, the man said he had "fought for every single one of your rights to express yourself."

"It's our First Amendment right to burn this flag regardless of what the president says," he added.

He then set fire to the flag, which had apparently been doused in accelerant.

Secret Service agents put the small fire out with an extinguisher, before detaining the man.

The US Park Police confirmed that it had made an arrest, citing regulations which forbid setting unpermitted fires in public parks such as Lafayette.

Trump's order

The Supreme Court held in a landmark 1989 ruling that burning US flags is protected by First Amendment freedoms, striking down prohibitions against desecrating the Stars and Stripes.

Both rulings were 5-4 and mixed along ideological lines.

Trump referenced the ruling on Monday, but argued there could be instances where flag burning falls into First Amendment exemptions, such as when it "is likely to incite imminent lawless action."

He directed the Justice Department to "prioritise the enforcement to the fullest extent possible" of laws related to flag burning.

It is unclear if the current Supreme Court, with a 6-3 conservative majority, would overturn or narrow the 1989 precedent.