She said it was important that other countries play by the rules, when it comes to cyber activity.
"It's important that we call out those who are not following the international rule book," she said, in reference to the Russian attacks.
National Leader Simon Bridges said what Russian has done is "despicable" and his party condemns its acts in this area.
"I ask for the Government to strongly condemn what Russia has been doing, because they have been soft on these issues in the past."
The "malicious cyber activity" targeted overseas political institutions, businesses, media and sporting organisations, the GCSB said.
"Our assessment found it was highly likely GRU was behind the campaigns and that a number of cyber proxy groups associated with these incidents are actors of the Russian state," Hampton said.
He added that these activities serve no legitimate national security interest to New Zealand.
"They were designed to negatively impact on the ability of people around the world to go about their daily lives free from interference.
"Such behaviour is unacceptable – it is counter to New Zealand's vision for an open, safe and secure cyberspace."
New Zealand organisations, however, were not directly affected by the attacks, the GCSB has confirmed.
But it is seeing a range of activity in New Zealand that contains indicators which can be linked to Russian state actors, Hampton said.
In light of the activity, the Government is taking a fresh look at the Cyber Security Strategy to ensure New Zealand is equipped to handle increasing cyber security threats.
"These incidents reinforce the need for New Zealand to have robust national systems to address cyber threats," Hampton said.
He adds that initiatives, such as the GCSB's CORTEX cyber defence capabilities and the proposed expansion of the Malware-Free Networks programme, help protect our nationally significant organisations.