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8chan is currently down after American cyber security firm Cloudfare dropped it as a customer.
However, Spark said if 8chan finds another host provider it will block access.
"We feel it is the right thing to do given the website's repeated transgressions and continual willingness to distribute disturbing material," Spark said.
The 8chan internet forum was used by the accused Christchurch mosque gunman to distribute his manifesto and livestream the attack.
8chan hosts message groups, and has been attacked for disseminating hate speech from white supremacist groups and inciting violence.
Spark said the government should step in.
"Appropriate agencies of government should put in place a robust policy framework to address the important issues surrounding such material being distributed online and freely available.
"But in the absence right now of such a policy framework... we believe the right thing to do right now is for us to block access to 8chan."
Spark, Vodafone, Vocus and 2Degrees, blocked websites which hosted content of the mosque attacks following the event and co-ordinated a response to global social media giants including Facebook and Twitter.