The action by the Supreme Court on Friday, which was presented without comment from the state’s justices, upheld rulings by two lower courts that stated the lawsuits could proceed.
They alleged in the lawsuits that during broadcasts of Infowars, Mr Jones defamed them and caused emotional distress by repeatedly disputing the authenticity of the shooting and the subsequent news coverage.
Six adults and 20 young students were killed in the shooting in 2012 at the Sandy Hook school in Newtown, Connecticut.
The four suits focused on various comments made by Mr Jones in the wake of the shooting, including his claims that it was “a giant hoax” and a “false flag” intended to help gain support for gun control measures, according to the Austin American-Statesman.
One of the suits focused on Mr Jones disputing a claim from the father of a six-year-old killed in the shooting, who said that he held his dead son in his arms in the aftermath.
While another noted statements made by Mr Jones where he claimed that the shooting was “as phony as a three-dollar bill” and that the parents were not actually grieving their dead children.
The ruling noted that two of the justices would have granted Mr Jones’ petition for review in the “false flag” lawsuit, but did not provide reasons for their dissent.
Lawyers for Mr Jones had argued that the host had been engaging in protected speech with his comments because he was discussing matters of public concern, according to the Statesman.
However, the parents claimed that he went further than that by accusing them of being actors working as part of a plan to limit sales of guns across the US.
Friday’s ruling also permitted a lawsuit to proceed against Infowars and reporter Kit Daniels by a man who was mistakenly identified as a suspect in the 2018 shooting at a high school in Parkland, Florida.
The photo of the man, who was not the shooter, remained on Infowars for 13 hours, and court records show that the website did not issue a correction after it was taken down.
Mr Jones is known for spreading conspiracy theories, including baseless claims that former Democratic nominee for president Hillary Clinton ran a child trafficking ring out of a Washington, DC pizza shop.
That claim gained widespread popularity online, and culminated in a man firing a gun inside the restaurant as he attempted to “self-investigate” the conspiracy theory.
Infowars has also faced bans from social media sites, including Facebook and YouTube for violating policies and spreading conspiracy theories.