US conspiracy theorist Alex Jones should pay parents of a child killed in the 2012 Sandy Hook massacre at least $US4.1 million ($5.9 million) for falsely claiming the shooting was a hoax, a Texas jury has ruled.

The verdict on Thursday followed a two-week trial in Austin, Texas, where Jones’s radio show and webcast Infowars are based.

The jurors will next consider the parents’ request for as much as $US75 million ($108 million) in punitive damages from Jones for spreading falsehoods about the killing of 20 children and six staff at Sandy Hook Elementary School in Newtown, Connecticut, on December 14, 2012.

Neil Heslin and Scarlett Lewis, separated parents of slain six-year-old Jesse Lewis, testified that Jones’ followers harassed them and sent them death threats for years in the false belief that the parents were lying about their son’s death.

During closing arguments on Wednesday, their lawyer Kyle Farrar urged jurors to end what he called their nightmare and hold Jones accountable for profiting off their son’s death.

Federico Reynal, an lawyer for Jones, acknowledged during his closing argument that Jones and Infowars reported “irresponsibly” on Sandy Hook but said his client was not responsible for the harassment.

Jones previously claimed that the mainstream media and gun-control activists conspired to fabricate the Sandy Hook tragedy and that the shooting was staged using crisis actors.

He later acknowledged that the shooting took place and sought to distance himself from previous falsehoods during the trial, telling jurors it was “crazy” of him to repeatedly make the claim that the shooting was a hoax.

He said that the shooting was “100 per cent real”.

In a surprising development, Mr Heslin and Ms Lewis’ lawyers revealed on Wednesday that Jones’ lawyers had inadvertently sent them two years worth of his texts and failed to request them back in time.

On Thursday, Judge Maya Guerra Gamel denied a motion for a mistrial by Jones’s lawyer who argued that lawyers for the plaintiffs should have immediately destroyed the records. The parents may now use the records as they wish.

In the second phase of the damages trial, both sides will present arguments on Jones’ net worth. A finance expert is set to testify for the parents. Jones is expected to return to the stand.

Jones’ company, Free Speech Systems LLC, declared bankruptcy last week. Jones said during a Monday broadcast that the filing will help the company stay on the air while it appeals.

Judge Gamble admonished Jones on Tuesday for not telling the truth about his bankruptcy and compliance with discovery during his testimony.

The parents’ lawyer also accused Jones of approaching the trial in bad faith, citing broadcasts where Jones said the trial was rigged against him and that the jury pool was full of people who “don’t know what planet they’re on.”

Mr Heslin and Ms Lewis joined other Sandy Hook parents in urging a judge to block Free Speech System from sending Jones or his companies any money until they get to the bottom of their finances.

The parents claim that Jones took $US62 million ($89 million) from the company while burdening it with $US65 million ($93 million) in “fabricated” debt owed to PQPR Holdings, a company owned by Jones and his parents.

Jones was set to stand trial in a similar suit in Connecticut in September, but that case is on hold while the bankruptcy proceeds.

The Sandy Hook gunman, Adam Lanza, 20, used a Remington Bushmaster rifle to carry out the massacre. It ended when Lanza killed himself with the approaching sound of police sirens.

-AAP