The Prime Minister welcomed Facebook's public commitment to do better at filtering hate speech but said an international commitment from governments and corporates is required.
The response needed to go beyond one company and one government, a spokesman for Jacinda Ardern said.
Global rules for social media platforms were needed.
She hoped that Facebook would back up its statement with meaningful and substantial action. "The proof will be in the pudding", the spokesman said.
Ardern had earlier called for Silicon Valley to take a stronger role in combating extremism in the wake of the Christchurch massacre and said she was "not interested in a PR exercise."
Opposition leader Simon Bridges said Facebook and other social media was used to promote the horrific shootings at two Christchurch mosques and it is appropriate that it reviewed its rules.
"Freedom of speech in a democracy means having to tolerate the expression of diverse views but violent hate speech is never acceptable," Bridges said.
Chief operating officer Sheryl Sandberg said that in the wake of the terror attack, Facebook was taking three steps: "strengthening the rules for using Facebook Live, taking further steps to address hate on our platforms, and supporting the New Zealand community."
It was also using existing artificial intelligence tools to identify and remove a range of hate groups in Australia and New Zealand, including the Lads Society, the United Patriots Front, the Antipodean Resistance, and National Front New Zealand.
New Zealand Muslim Association President Ikhlaq Kashkari said they welcomed social media companies taking a more responsible approach and looked forward to seeing the result.
"We are keen to see how this works in practise."
Chief Censor David Shanks, who officially banned the 16-minute and 55-second video last week, labelling it as "objectionable", said the changes announced by Facebook were in many respects too late.
Reports he had seen indicated that the social media company had been on notice for sometime and that their policies and enforcement were ineffective.
Though he supports changes, more needs to be done, Shanks said.
"I think regulation will form an essential part of any effective response, alongside international agreement on where the lines are and how we enforce them."
Dr Stuart Lange, speaking on behalf on the New Zealand Christian Network, said Christian people have often been concerned about the negative impact of some material on social media platforms.
"They were sickened that the perpetrator had been able to live stream his horrific actions to the world.
"They will no doubt be very pleased to learn that Facebook is trying to tighten its processes.
"Although it is important for societies to protect freedom of belief and expression, incitements towards racism, hatred,violence and terrorism must never be accepted."