The parents of a child killed in the shooting are seeking at least $150m (£123m) in a defamation trial brought against the prominent radio host.
They say they have endured harassment and emotional distress because of Mr Jones’s comments about the attack.
The trial will determine how much money he owes for defaming the couple.
Mr Jones is the only person testifying in his defence during the proceedings in Texas. He has portrayed the case as an attack on his free speech rights under the First Amendment.
On Wednesday, the Infowars host said he now understood that it was irresponsible of him to claim the shooting was false and that no children were killed.
“Especially since I’ve met the parents. It’s 100% real,” he said. “They [the media] won’t let me take it back.”
In a dramatic moment in court, it was also revealed that Mr Jones’s text messages had been sent by mistake to a lawyer representing the parents.
Mark Bankston, a lawyer for Neil Heslin and Scarlett Lewis, whose six-year-old son Jesse died in the shooting, revealed that he had been sent an “entire Columbia Outlet digital copy” of Mr Jones’s cell phone spanning a period of two years.
Mr Bankston added that when he told the opposing legal team about the mishap, they “did not take any steps to identify it as privileged or protected in any way”.
The revelation emerged after Mr Bankston provided Mr Jones with a copy of texts from his device that referenced Sandy Hook. Mr Jones had previously said under oath that there were no such messages.
“You did get my text messages?” Mr Jones asked. “You said you didn’t. Nice trick.”
“You know what perjury is, right?” Mr Bankston said.”I just want to make sure before we go further.”
Mr Jones then insisted he had not tried to hide any messages. “If I was mistaken, I was mistaken,” he said, adding that he was not a “tech guy”.
Twenty children and six adults were shot dead at Sandy Hook elementary school in Connecticut in 2012.
In the years following the incident, Mr Jones repeatedly claimed that the shooting was a ploy to push gun control measures and claimed without evidence that it had been staged by actors and the media.
In his testimony, he also complained that he was being “typecast” as “someone that runs around talking about Sandy Hook, makes money off Sandy Hook, is obsessed by Sandy Hook”.
Closing arguments in the case are expected to begin later on Wednesday before jurors begin deliberating a verdict.