Conspiracy theorist Alex Jones hit out at critics as he testified in a trial to determine how much he owes families of victims who died in the 2012 Sandy Hook Elementary School mass shooting, which he falsely claimed was a hoax.

Tensions boiled over after roughly four hours of testimony in the Waterbury, Connecticut courtroom, not far from Newtown, the town where the massacre took place.

Mr Jones fulminated against "liberals" and refused to apologise to a packed gallery of victims' families.

"These are real people, do you know that Mr Jones?" a lawyer for the families, Chris Mattei, asked.

"Just like all the Iraqis you liberals killed and love,"retorted Mr Jones, a Texas-based webcast host who is being sued because he said no one was killed at Sandy Hook and the families were merely actors.

Many of his followers then tormented and threatened the families.

The defamation trial concerns only how much Mr Jones and the parent company of his Infowars site must pay in damages for spreading lies that the US government staged the killing of 20 children and six staff members as a pretext for seizing guns.

The testimony triggered a three-way shouting match between Mr Jones, Mr Mattei and Mr Jones' lawyer, Norman Pattis, who repeatedly objected to Mr Mattei's questioning.

After jurors left for the day, Judge Barbara Bellis told the attorneys that she would enforce a "zero tolerance" policy for disruptions and would hold contempt-of-court hearings for anyone who "steps out of line," including Mr Jones.

Mr Mattei played a video clip in which Alex Jones praised his followers for placing Infowars stickers around the Connecticut courthouse.

"Conservatives put up stickers and we're bad, I know, we all need to go to prison," Mr Jones said in a mocking tone on the witness stand, prompting the judge to briefly clear the courtroom and hold a discussion with attorneys. Alex Jones does not face any criminal charges.

The clip was played as Mr Mattei presented evidence that Mr Jones' followers had harassed Sandy Hook families online and in person, including at memorials for victims.

Alex Jones also acknowledged calling Judge Bellis a "tyrant" after Mr Mattei displayed an image posted on Infowars depicting the judge with red lasers shooting from her eyes. He said he was not responsible for the post.

Judge Bellis has largely barred discussion of politics and conspiracy theories at the trial.

Alex Jones is also not permitted to dispute his liability for damages, after the judge issued a default judgment last year because he repeatedly failed to comply with court orders.

Jurors must decide only what Mr Jones and Infowars' parent Free Speech Systems must pay the plaintiffs, who also include an FBI agent, for the pain and suffering they say he caused.

A month ago, the conspiracy theorist was hit with a $49.3 million verdict in a similar case in Texas, where Free Speech Systems is based.

Alex Jones' lawyers hope to void most of the payout, calling it excessive under Texas law.