Activists have taken issue with the South Dakota monument to former US presidents, which has been constructed on land sacred to the Sioux tribe.
Mr. Trump will deliver fighter jets and fireworks to Mount Rushmore about 3 July because his campaigning tour persists.
The contentious trip comes amid heightened racial tensions nationally.
However, the land the memorial is based on – the Black Hills of South Dakota – has been obtained in the native Lakota Sioux by the US authorities from the 1800s.
Some Native American activists say the land ought to be returned to the Sioux and the monument brought down. Other people state native groups should get economic benefits from tourism to the website.
Oglala Sioux President Julian Bear Runner advised that the Argus Leader newspaper that Mr. Trump didn’t consult with tribal leaders in his trip.
Still, another tribe member and neighborhood activist Nick Tilsen told the Associated Press that the monument” is a symbol of white supremacy, of structural racism that is alive and well in society now”.
“It is an injustice to steal Indigenous people’s land then split the white faces of those conquerors who perpetrated genocide.”
The row over Mr. Trump’s trip comes as, around the united states, statues of leaders who have ties to captivity have come down from the aftermath of this George Floyd protests.
The president is expected soon to sign an executive order to earn any vandalism or destruction of people statues and national monuments punishable by prison time.
On Thursday evening also told a Fox News town hall in Green Bay, Wisconsin: “Every night we are likely to get harder and harder [on statue protesters] and at some stage, there will be retribution since there must be.
“These people are vandals, however, they are agitators, but they are really, they are terrorists in ways.”
Monuments to George Washington and Thomas Jefferson – that owned slaves – are one of the ones which were eliminated or torn down.
A statue of Theodore Roosevelt, including the former president flanked by a Native American man and an African guy, at New York is also to be eliminated – a strategy Mr. Trump is known as”ridiculous”.
However, South Dakota’s Republican Governor Kristi Noem refused the idea that Mount Rushmore will be following, tweeting: “Not on my watch”
Mr. Trump’s planned trip made headlines earlier this month for his choice to sponsor the very first fireworks at Mount Rushmore in over ten years, despite environmental issues.
The monument is surrounded by a federal forest and some fear the screen can set off wildfires from the dry brush.