Democratic Del. Eleanor Holmes Norton, who is Black, said she will introduce a bill in the House next week to have the two statues removed from federal land in the District -- Jackson's from Lafayette Park across from the White House and Lincoln's from near the Capitol.
The showdown comes as protesters claim they will try to take down the Lincoln statue Friday night and after Trump's promise to sign an executive order "before the end of the week" to make it easier to prosecute those who target statues with "long-term jail time."
It also happens amid a nationwide reckoning with the country's racist foundation in the wake of George Floyd's death.
"I think many of the people that are knocking down these statues don't even have any idea what the statue is, what it means, who it is," Trump said Wednesday in the Rose Garden. "Now they're looking at Jesus Christ. They're looking at George Washington. They're looking at Abraham Lincoln. Thomas Jefferson. Not gonna happen. Not gonna happen, not as long as I'm here."
Holmes Norton says she's well aware of the history of the statues she's fighting to take down.
The "Emancipation Memorial," which sits in Lincoln Park near the Supreme Court and U.S. Capitol, depicts a heroic Abraham Lincoln with his hand symbolically giving the blessing of freedom over a kneeling newly freed slave.
She doesn't have an issue with Lincoln himself, who ended slavery, but with the way the statue was created and the power relationship depicted, saying it was "controversial from the start" and that it belongs in a museum instead.
"Although formerly enslaved Americans paid for this statue to be built in 1876, the design and sculpting process was done without their input, and it shows. The statue fails to note in any way how enslaved African Americans pushed for their own emancipation. Understandably, they were only recently liberated from slavery and were grateful for any recognition of their freedom," she said.
She notes that Frederick Douglass, in his keynote address at the statue's unveiling, also expressed his displeasure.
Holmes Norton also has called for the removal of the Jackson statue from Lafayette Park -- a replica of which Trump has placed behind his desk in the Oval Office -- after protesters failed to take it down Monday night.
"This prominent location in the nation's capital, right outside of the White House, should never have honored a man who owned slaves and was responsible for the deaths of roughly 4,000 Native Americans," she said in a statement. "Jackson's entire tenure is a shameful part of our history, and I will see to it that he is no longer honored with a statue in Lafayette Park."
President Trump, who has called himself a "fan" of Jackson, responded to the protests by threatening jail time via Twitter. Additional fencing and barricades were placed in Lafayette Park the following morning.
Trump has ramped up his rhetoric against what he calls "vandals, hoodlums, anarchists and agitators" attacking statues.
He scolded states Wednesday evening for allowing "roving gangs of wise guys, anarchists & looters" to remove statues, saying "all represent our History & Heritage, both the good and the bad."
While Trump and Holmes Norton disagree over what happens to the statues, a clash between protesters and police could come soon.
At least one group called "The Freedom Neighborhood" has made plans to return to Lincoln Park Friday night and attempt to remove the statue, after a Tuesday night protest where they argued the government has dismissed calls for its removal for years.
"This statue right here embodies the white supremacy and the disempowerment of black people that is forced upon us by white people. That is why we are tearing this statue down," said 20-year-old organizer Glenn Foster on Tuesday, before the group vowed to return Friday at 7 p.m.
Trump hasn't directly responded yet to calls to remove the Emancipation Memorial just miles from the White House, but he's certainly aware of the protests in the District.
After a statue of Confederate Gen. Albert Pike was torn down and burned by protesters on Juneteenth outside D.C. police headquarters, Trump reportedly instructed Interior Secretary David Bernhardt to put it back up, according to NBC News.
"It is the intent of the National Park Service to mitigate any damage to any statue, monument, or memorial damaged due to any criminal activity," Alexandra Picavet, acting chief spokesperson, said in a statement to ABC News Thursday.
The White House late Wednesday declined to comment, but it appears Trump and Bernhardt are on the same page.
Following Monday's protests and attempts to remove the Jackson statue, Bernhardt -- who runs the agency charged with protecting public lands -- issued a statement condemning the scene.
"I just left Lafayette Square where another so-called "peaceful protest" led to destruction tonight. Let me be clear: we will not bow to anarchists," the statement released Tuesday read. "Law and order will prevail, and justice will be served."
Officials say the D.C. National Guard remains on standby, if needed, to protect the statues.
ABC News' John Parkinson, Stephanie Ebbs and Ben Gittleson contributed to this report.