Tunsil spoke at a news conference after his draft selection in Chicago and an alleged hack of his Instagram and Twitter accounts.
"I'd have to say yeah," Tunsil said when asked by a reporter if he took money from a coach.
A screenshot of a text that was published to the Instagram account @kingtunsil appeared to show a request for money from Ole Miss assistant athletic director John Miller for rent and so Tunsil's mother could pay her $305 electric bill.
"Those were true," Tunsil said. "I made a mistake of that happening."
Two questions later, as he was being asked a follow-up question about whether he had spoken to NCAA investigators, Tunsil was ushered out of the news conference by an official.
"He hasn't seen anything," the official said as they walked off the stage. "This all happened while he was up here."
In the alleged text messages, Miller responds to the request for rent by replying "See Barney next week," an apparent reference to Ole Miss assistant athletic director for high school and junior college relations Barney Farrar.
Farrar told ESPN's Joe Schad that he has not given Tunsil money and that Tunsil did not ask him for money. According to Farrar's Ole Miss biography, he "plays a vital role in recruiting, which has helped Ole Miss land three straight top-15 signing classes."
Ole Miss released a statement saying it was aware of the story.
"Like we do whenever an allegation is brought to our attention or a potential violation is self-discovered, we will aggressively investigate and fully cooperate with the NCAA and the SEC," the school said in the statement.
Ole Miss athletic director Ross Bjork told ESPN's Edward Aschoff on Friday that the school won't have further comment until they hear from Tunsil and see what sort of clarification he provides about the text exchange and what supposed money he received.
An Ole Miss official told ESPN on Friday morning that the school was trying to verify whether the alleged text messages between Tunsil and Miller are authentic. The official said Miller also served as a liaison for athletes to receive money from the Ole Miss Opportunity Fund, which is available to students from low-income families to fill the gap for their educational and housing expenses.
It wasn't immediately clear whether using the fund to pay Tunsil's mother's rent and utility bill would be permissible under NCAA rules.
Rebels coach Hugh Freeze and Jimmy Sexton, Tunsil's agent, both of whom attended the draft Thursday in Chicago, couldn't immediately be reached for comment.
Tunsil's Instagram account has been deleted.
Ole Miss received a notice of allegations from the NCAA in January. The school hasn't released many details about the investigation.
Tunsil, who was considered the potential No. 1 pick in the draft until recently, was suspended by the NCAA for the first seven games last season for accepting improper benefits.
The NCAA determined that Tunsil improperly used three loaner cars without paying during a six-month period, received two nights of lodging at a local home, accepted an airline ticket purchased by a friend of a teammate and used a rental car for one day without paying. The NCAA also alleged that Tunsil received an interest-free, four-month loan to make a $3,000 down payment for a used car.
NCAA investigators said Tunsil, from Lake City, Florida, wasn't initially forthcoming during the investigation about his use of the vehicles.
The NCAA launched an investigation into improper benefits after Tunsil and his stepfather, Lindsey Miller, filed domestic charges against each other last year. Tunsil said he attacked Miller after his stepfather assaulted his mother, Desiree Polingo. Miller said Tunsil's attack was unprovoked and that he was trying to stop his stepson's contact with agents. The criminal charges against both men were dropped in August.
On Tuesday, Miller filed a civil lawsuit against Tunsil in Lafayette County Court in Oxford, Mississippi, alleging that Tunsil defamed his character and caused "intentional infliction of emotional distress."
Miller's attorney Matthew Wilson told ESPN on Friday that his client was not responsible for leaking the video of Tunsil smoking from the bong on Twitter, which was posted shortly before the draft started Thursday night before being deleted.