In the same tweet, the president also blasted NASCAR for banning Confederate flags from all raceways.
A Richard Petty Motorsports crew person saw and reported an apparent noose on June 21 in a Talladega Superspeedway garage that was assigned to driver Bubba Wallace and his team.
Wallace has been vocal about his support for the Black Lives Matter movement and pushed NASCAR to remove Confederate flags from all sanctioned events, a decision the company announced shortly before the crew member found the rope.
NASCAR alerted the FBI and the agency conducted an investigation. Investigators determined it was a pull rope fashioned like a noose and had been there since October before Wallace was assigned to the garage.
Wallace said he stood by the FBI's conclusion and NASCAR's statement of support, but Trump on Monday tweeted that the driver should apologize to everyone involved and called the incident "a hoax." He added that the noose investigation and the decision to remove Confederate flags from raceways "caused the lowest ratings EVER," without any citation.
On Saturday, NBC earned a 1.1 rating and 1.692 million viewers, including streaming, for NASCAR’s Xfinity Series race at Indianapolis, making it the most-watched Xfinity race from the location in three years, according to NBC Sports and Nielsen ratings. Ratings for Sunday's race at Indianapolis were up 46% over last year's event, NASCAR told ESPN.
Wallace responded to Trump on Twitter later in the afternoon with a message to "To the next generation and little ones following my foot steps."
"Always deal with the hate being thrown at you with LOVE! Love over hate every day. Love should come naturally as people are TAUGHT to hate. Even when it's HATE from the POTUS...Love wins," he said in the tweeted image.
NASCAR also released a statement Monday staying that it "continues to stand tall with Bubba, our competitors and everyone who makes our sport welcoming and inclusive for all racing fans."
Over the last few weeks, other NASCAR drivers and NASCAR President Steve Phelps have shown Wallace their support. Before the start of the race following the apparent noose's discovery, various drivers helped push Wallace's car to the starting line in a symbolic gesture.
On Monday, NASCAR driver Tyler Reddick fired back at the president with a tweet saying drivers didn't need an apology.
"We did what was right and we will do just fine without your support," he tweeted, along with a gif that showed footage from a play where a character portrayed by Denzel Washington closes the door on a white character.
When asked about the tweet during an appearance on Fox News later in the morning, White House Press Secretary Kayleigh McEnany defended the president. She brought up examples of questionable hate crime reports such as the case of Jussie Smollett, who has been accused of staging a racist and homophobic attack on himself.
"The president is making a broader point that judging before the facts are out is not acceptable," McEnany contended.
During the White House news conference later in the afternoon, McEnany ignored reporters' questions about Trumps tweet and falsely claimed that Wallace didn't accept the FBI's findings.
Sen. Lindsey Graham, however, defended NASCAR's decision to remove the Confederate flag from events. During an interview with Fox News radio Monday, the Republican senator said the flag was "not a good way to grow business."
Graham added that Wallace had nothing to apologize for.
"When there was a chance that it was a threat against Bubba Wallace they all rallied to Bubba's side," the senator said, referring to other drivers. "So I would be looking to celebrate that kind of attitude more than being worried about it being a hoax."
NASCAR's Phelps has said the company would continue to investigate the incident, and Wallace tweeted on June 24 that he was grateful the community and investigators took the situation seriously.
"Make no mistake, though some will try, this should not detract from the show of unity we had on Monday and the progress we've made as a sport to be a more welcoming environment for all," he tweeted.
ABC News' Alyssa Acquavella and Jordyn Phelps contributed to this report.