However, he said the approach can only ever be a temporary solution to what it sees as a bigger problem.
"Like most New Zealanders, we were shocked and saddened by the weaponisation of social media in the terrorist attack in Christchurch on March 15, and, alongside other ISPs, we took the unprecedented step to block access to abhorrent sites promoting extremist content in the immediate period following," said Llewellyn.
"We urge the Government to speed up the current process under way to develop a broader and more formal framework to address extremist content online.
"Vodafone already opts-into the current filter that is in place for child exploitation, so we support the Government's announcement to invest in mandatory or voluntary measures to keep New Zealanders safe from terrorist and violent extremist content on digital channels."
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Llewellyn says Vodafone NZ will continue to engage with government and non-governmental agencies, online platforms and civil society, about how the mechanism might apply.
Key questions, he says, include who will determine what constitutes as extremist content, how the filter can be applied, and will it be able to differentiate between legitimate use and extremist content hosted on the same site.
Yesterday, the Chief Censor also outlawed a document said to have been shared by the terrorist who killed two people in Halle, Germany last month.
Shanks said the two publications, designed to encourage people to commit terrorist acts against innocent people and minority groups, have no place in New Zealand.
"These publications promote killing and terrorism and serve no positive purpose," he said.
Within days of the March 15 attack, the alleged gunman's manifesto and livestream video of the shootings were classified as objectionable by the Censor's office.
Internal Affairs' director digital safety, Jolene Armadoros, urged New Zealanders to think about their online safety.
"We are committed to keeping New Zealanders safe from harm through the prevention and detection of objectionable content, and by educating Kiwis on how to keep themselves and their whānau safe online," she said.
Sharing, hosting and downloading objectionable content is an offence under New Zealand law. Anyone who has concerns they have seen something illegal, can email censorship@dia.govt.nz.