Conspiracy broadcaster Alex Jones must pay $US473 million ($A724 million) in punitive damages on top of a nearly $US1 billion verdict handed down last month for his defamatory claims about the 2012 Sandy Hook mass shooting, a Connecticut judge has ruled.

The ruling comes a month after a jury in Waterbury, Connecticut, found Jones must pay more than a dozen relatives of Sandy Hook victims $US965 million in compensatory damages for falsely claiming they were actors who staged the shooting as part of a US government plot to seize people’s guns.

On December 14, 2012, a gunman murdered his mother, then killed 20 children and six staff members at Sandy Hook Elementary School before killing himself.

The conspiracy theories amplified by Infowars on its website, social media and a show hosted by Jones led to years of threats and other harassment of the parents of the murdered children.

The plaintiffs had asked a judge to impose additional punitive damages, citing what they said was the “historic” scale of Jones’ wrongdoing and his “utter lack of repentance”.

Jones has since acknowledged the shooting took place but refused to apologise to the families during his trial testimony.

In a statement, plaintiffs’ lawyer Chris Mattei said the ruling “serves to reinforce the message of this case: those who profit from lies targeting the innocent will face justice”.

Jones’ lawyer, Norm Pattis, did not immediately respond to a request for comment.

In recent court filings, he has argued for a new trial or substantial reduction of the verdict.

In a separate order late on Wednesday, state Judge Barbara Bellis temporarily blocked Jones from moving any personal assets out of the country.

The ruling came at the request of the plaintiffs, who claim Jones is trying to hide assets to avoid paying.

Jones’ company, Free Speech Systems LLC, is also liable for the verdict.

It filed for bankruptcy in Texas in July.