"Public access to computers in our libraries is being accessed by schoolchildren who log into these games.
"I understand from our library staff that we cannot block such access to websites ourselves at our local level.
"We are locked into a national consortium managed by the National Library."
The National Library of New Zealand confirmed in a statement that it provides internet access to public libraries through the Aotearoa People's Network Kaharoa (APNK) service and said, "APNK has a commercial filter in place to block objectionable material".
"I don't think it's the intention of our public service to provide such access as part of our commitment to the benefits of open education," Gurunathan said.
"Primary school children should especially not be able to access such games.
"At the most, responsibility for such access should be a private decision made through parental guidance."
Following a complaint at a Kāpiti library, staff have placed notices by all public computers at all Kāpiti libraries asking that, out of respect, such violent games are not played on them.
Staff have also spoken directly to regular users of these games and where possible to the parents.
In the meantime staff are seeking a long-term national policy decision from the National Library.
The National Library of New Zealand said in a statement, "As new sites are popping up all the time we block inappropriate access.
"The manager of Kāpiti Libraries has been in touch with us about sites of concern, and we are actively looking into this specific case."