This included "adult content, harmful and stealth content, and hacking content," Morgan said.
If library users thought blocked websites were not objectionable, library staff could provide manual exceptions.
Hamilton's public library internet users are banned from looking at websites containing porn, torture, cruelty, violence or bullying or anything that promotes exploitation of children for sexual purposes.
Access to sites that promote criminal acts or terrorism, or those which represent any class of society as being inferior to others is also prohibited.
The policy is similar in Tauranga, where kids younger than 16 need a signed consent form from a parent or caregiver to access the net.
In Wellington, the right is reserved to deny access to people misusing library internet services through cyber bullying and harassment, illegal downloading or accessing porn and other objectionable material and Christchurch and Dunedin libraries use filtering software as in Auckland.
The inability to access some tabloid media sites is on the flipside of the library's stance last year against the pulling of Ted Dawe's controversial teen novel Into the River from shelves around New Zealand.
Also in 2015, the council was criticised for a flaw which allowed its Wi-Fi users to access pornographic images through Google image searches.