It comes after the former president decried the removal of the Confederate monument in Richmond, Virginia.
According to state officials, the time capsule is believed to be buried in or around the cornerstone pedestal of the former Robert E. Lee statue.
"I wonder what @GOPLeader [Kevin McCarthy] thinks of this statement?" the Illinois Republican asked.
Historians doubt it is an actual photograph of Lincoln's body because the only known photo was taken in City Hall in New York on April 24, 1865.
On Wednesday, Trump started off the statement by stating that watched as a "massive crane took down the magnificent and very famous statue of 'Robert E. Lee On His Horse' in Richmond, Virginia. It has long been recognized as a beautiful piece of bronze sculpture."
"Any remnant like this that glorifies the lost cause of the Civil War, it needs to come down," Virginia Governor Ralph Northam said.
The statue's removal comes 131 years after it was erected. The statue will be placed in storage at a state-owned facility while its future is determined.
The ban was issued for "special security reasons," the Federal Aviation Administration said.
The carving on the side of Stone Mountain in Georgia of Jefferson Davis, Robert E. Lee and Stonewall Jackson is the biggest Confederate memorial in the world.
The statue will come down on Wednesday, September 8, 131 years after the statue was put in place. It will be placed in storage until its future is determined.
"Today is an historic day in Virginia. Today, we turn the page to a new chapter in our Commonwealth's history," said Virginia Attorney General Mark Herring said in a statement.
The state senator appeared to be responding to the Cleveland Indians' decision to rename the team Cleveland Guardians.
The statue was taken down nearly four years after a white supremacist rally against the statue's initial proposed removal turned violent.
The city will remove two Confederate statues nearly four years after a white supremacist rally against their initial proposed removal left three dead.
The West Point Association of Graduates tweeted that Robert E. Lee had assisted Union General Gordon Granger in proclaiming slaves had been freed following the end of the Civil War.
A statue honoring Confederate General Robert E. Lee was quietly removed from the U.S. Capitol overnight Sunday, but statues honoring Confederate leaders and others with racist pasts remain—months after leaders of Congress urged their removal.
"Robert E. Lee was a traitor whose actions murdered American troops. Why are you so clueless about America and our history?" replied one irate student of history.
Police in Richmond, Virginia were called to investigate a report of an unoccupied vehicle being struck once by gunfire near the city's Robert E. Lee statue.
"They're ripping down our history," President Donald Trump said of U.S. protesters. "That's where these guys begin. They take away your history."
"Much of the racial tension, strife and protest we're seeing across the country emanates from right here in Charlottesville," community organizer Don Gathers said. "But now we're moving the needle in a positive way."
"This is public property. This is my city," the woman shouts, appearing to push one person away. Someone behind the camera then called her "a racist," asking her to leave.
Reverend Robert Wright Lee said he supports a bill that proposes removing a statue of his ancestor, Confederate General Robert E. Lee, from Antietam National Battlefield in Maryland.
A look back at the Civil War ought to be most instructive.
The move may be related to protests against police brutality and racism that have erupted throughout the U.S. after the May death of Minneapolis resident George Floyd.
"Enough's enough, man," Biden said at a rally in Iowa. "This is nonsense."
"The president is now glorifying a loser," Congressman James Clyburn pointed out on Sunday. "Robert E. Lee was a loser," he asserted.
"You have a gap in your teeth. We are part of the master race, don't ever forget that," said Leavenworth County Commissioner Louis Klemp.
Some community members criticize the name change for the acronym spelling out the Confederate general's name
Yale University and a former State Representative in Georgia are pointing the way to healing in America as the debate over Confederate monuments rages.
"We don't want people to think that they can hide behind Robert E. Lee's name for these senseless acts of violence."