"We are going to do an executive order and make the cities guard their monuments," Trump told Eternal Word Television Network's Raymond Arroyo. "This is a disgrace."
Arroyo, who is also a Fox News contributor, played a clip of the interview on Monday's edition of "The Ingraham Angle."
"It's a disgrace," Trump repeated. "Remember, some of this is great artwork. This is magnificent artwork, as good as there is anywhere in the world, as good as you see in France, as good as you see anywhere. It's a disgrace.
"Most of these people don't even know what they're taking down," the president added.
Trump told Arroyo he was particularly disturbed by the toppling Friday of a San Francisco statue of Ulysses S. Grant, commanding general of the United States Army during the final 13 months of the Civil War.
"You saw it ... where they want to take [Grant] down. He's the one who stopped the ones that everyone dislikes so much," said Trump, referring to Confederate military officers whose statues have also been vandalized and destroyed.
Arroyo told host Laura Ingraham that the president did not elaborate on how the order would be crafted. The EWTN anchor posited that Trump could designate the statues as National Historic Landmarks or enter them in a "national trust" to legally protect them.
"It is certainly something he's clearly got on his mind," Arroyo said. "I'm sure the White House counsel's office is working on it. That is big news that we haven't heard yet, [that] there is an executive order forthcoming.
"It is a question, certainly in my mind, how the federal branch can impose its will on these cities and municipalities," Arroyo added.
Monday night, hours after Arroyo interviewed Trump, a group of protesters attempted to pull down a statue of Andrew Jackson in Washington D.C.'s Lafayette Park before being pushed back by police.