Cook said the changes were a good first step, but the co-founders wanted to establish the group to give a voice to the majority of New Zealanders who want change.
"Parliament recently banned most semi-automatic weapons, but until there is full control of these weapons, and a register of all guns, the risk remains of them falling into the wrong hands," Cook said.
"Gun Control NZ will give voice to the majority of New Zealanders who want to ensure the next generation inherits a country free from the danger of gun violence."
Gun licences currently have to be renewed every 10 years, but Gun Control wanted to shorten that to three years.
Yasbek said hunting and shooting sports had a long history in New Zealand.
"We support properly vetted people being able to own registered rifles and shotguns, so long as those guns are not semi-automatic."
The Government is currently working through the second round of gun law reform, which will look at whether a national register of firearms is needed, the vetting process for a "fit and proper" person to obtain a gun licence, and the police inspection and monitoring regime, including rules around storage.
Previous reports, including one in 1997 by retired judge Sir Thomas Thorp, called for a national register of guns, but successive Parliaments did not have the will or the support to put one in place.