President Trump signaled Tuesday that calls to remove Confederate-era symbols could be a slippery slope that leads to the demise of statues depicting Presidents George Washington and Thomas Jefferson.

"George Washington was a slave owner. Was George Washington a slave owner? So, will George Washington now lose his status? Are we going to take down statues to George Washington?" Trump asked reporters during a press conference at Trump Tower in New York City. "How about Thomas Jefferson? What do you think of Thomas Jefferson? You like him? OK good. Are we going to take down his statue? Because he was a major slave owner. Are we going to take down his statue?"

Trump took questions from reporters during an event at Trump Tower, where he announced a new executive order on infrastructure projects.

But the president spent most of the impromptu press conference answering questions from reporters about the events in Charlottesville, where white nationalists gathered Saturday to protest the removal of a statue of Civil War general Robert E. Lee.

Despite the violence that broke out between white nationalist groups and counter-protesters, Trump said there were other "very fine people" who were in the Virginia city opposing removal of the "very, very important" monument and the renaming of a park who were not associated with the white nationalist groups who rallied there.

"You had some fine people," Trump said of both sides involved in clashes in Charlottesville, "but you also had some troublemakers, and you see them come with the black outfits and with the helmets and with the baseball bats, you had a lot of bad people in the other group."

The president said he condemned the neo-Nazis and white nationalists who clashed with counter-protesters in Charlottesville, as he did during remarks Monday, but said efforts to remove Confederate-era symbols were attempts to change history and culture.

"You're changing history. You're changing culture," Trump said. "And you had people, and I'm not talking about neo-Nazis and the white nationalists because they should be condemned totally, you had many people in that group other than neo-Nazis and white nationalists, and the press has treated them absolutely unfairly."

After violence erupted in Charlottesville on Saturday, elected officials on both sides of the aisle have called for cities and states to remove Confederate monuments.