SACRAMENTO — A day after he was shoved by an anti-vaccine activist who streamed the incident live on Facebook, state Sen. Richard Pan said social media companies should be held responsible for allowing violent discourse that can inspire real-life attacks.

“Facebook is deliberately giving a platform to this violence, and perhaps inciting another person to do the same, maybe even up the ante,” the Sacramento Democrat said during remarks Thursday on the Senate floor.

Sacramento police arrested Kenneth Austin Bennett, 54, who is active in the campaign against mandatory childhood vaccines, after he confronted Pan on a downtown Sacramento street Wednesday about his bill to tighten the rules for obtaining a medical exemption from the shots required by California schools. Bennett, who recorded himself pushing Pan from behind live on Facebook, was cited for misdemeanor battery and released.

Pan said he asked Facebook to take down the video, but the company refused because “it’s not violent enough.”

Facebook, in a statement, said it has “community standards” against inciting violence and coordinating harm and removes anything that violates those standards.

“We want everyone using Facebook to feel safe,” a spokesperson said. “In this instance, after a thorough investigation, we determined there was no basis to remove the video as it does not violate our policies.”

In an email to one of Pan’s staff members, Facebook said “pushing is low severity violence which is not covered under” its standards. Other comments made by Bennett were “not a direct threat,” the company said.

Pan has received a torrent of online abuse and threats since he carried legislation in 2015 to eliminate personal belief exemptions for mandatory vaccines. In an interview, the senator said Bennett shoving him was the natural result of years of dehumanizing memes placing a target on his face or comparing him to Adolf Hitler.

In the Facebook live video, Bennett said that if Pan “got what he deserved, he would be hanged for treason for assaulting children, for misrepresenting the truth.”

Pan said he worried about a future attack by someone who saw the adulation that Bennett received in the comments on his video. When social media companies disseminate violent content and give it an audience, Pan said, they should be liable for the consequences, the same way a newspaper could be if it published an ad calling for someone to be hanged for treason.

“Facebook groups allow them to create an echo chamber and rile each other up,” he said. “This is toxic to our public discourse.”

Pan pursued a bill last year that would have required the state attorney general to draft a strategic plan for social media companies to fight the spread of misinformation on their platforms. It was vetoed by then-Gov. Jerry Brown.

Pan said he was not yet considering legislation related to violent rhetoric on social media, but that the issue needed to be studied.

“Ideally, it would be good if the social media companies looked at it much more closely,” he said.

Alexei Koseff is a San Francisco Chronicle staff writer. Email: alexei.koseff@sfchronicle.com Twitter: @akoseff