The New Zealand Superannuation Fund, ACC, the Government Superannuation Fund Authority, the National Provident Fund, and Kiwi Wealth put out a joint statement late Wednesday saying the social media companies should "fulfil their duty of care to prevent harm to their users and to society".
NZ Super Fund chief executive Matt Whineray said they had been profoundly shocked and outraged by the Christchurch attacks and their transmission on social media.
"These companies' social licence to operate has been severely damaged," he said.
The move is being backed by KiwiSaver providers, with some taking steps already.
KiwiSaver fund manager Milford Asset Management dumped its $14 million shareholding in Facebook on Monday.
Milford chief executive Mark Ryland said Facebook, Google and Twitter must take action following the livestreaming and content sharing on social media of the mosques attacks.
"Not acknowledging any responsibility for their platforms is not acceptable," Ryland said. "Social media companies need to provide genuine assurance around their course of action."
Others have joined their voices to support the government-backed funds but say they won't be selling the shares for now.
Bruce McLachlan, Fisher Funds chief executive, said it had advised both Facebook and Google that it was very unhappy about their inability to keep footage of the events in Christchurch off their platforms.
"We have sought to engage with them to understand how this has happened and what investments they are making to ensure this cannot happen again in the future."
McLachlan said it had chosen not to take any action beyond that at this time because the other side of the social media argument was that these platforms also did a tremendous amount of good.
"In the wake of terror attacks globally it has been a place for people to mark themselves as safe, get in touch with loved ones, organise events/fundraising, and otherwise support those impacted.
"More broadly it allows the public to communicate with friends and family, engage with their communities and become better informed about the world around them."
McLachlan said the debate on social media had a long way to go.
"These platforms need to ensure they are doing all they can to protect users and the broader community, while still allowing people to benefit from the increased connectedness these tools provide."
He said investment was about making long-term quality decisions in clients' best interests that were considered and balanced.
"The decision on social media companies investment is no different, and will remain under review."
Booster principal David Beattie said it had reached out to the Super Fund and confirmed its support.
He said joining with other investors was a great example of how collective shareholder action could look to make change.
Beattie said if there was a determination that Facebook had broken the law by livestreaming the Christchurch attack it would take that into account in its investment decisions.
"But we won't be doing a knee-jerk reaction at this point," he said.
Beattie said he was confident other global investors would come on board and support the Super Fund given the global reaction to the event.
Sam Stubbs, managing director of Simplicity, said it also got in touch with the Super Fund to give its support but would not be selling shares.
He said it was much more powerful to be in the boardroom of a company to try and initiate change.
Stubbs said the Super Fund's stance was key as "no dollar was more valuable to any company than a Sovereign wealth fund".
Anne-Maree O'Connor, head of responsible investment at the Super Fund, says its preference is to engage and use its influence as a shareholder to encourage the companies to take action.
"We have more leverage to progress these issues by holding shares and actively engaging and voting than by divesting."
She is optimistic that it will be able to bring other major investors on board and noted that combined pressure from a large number of investors had a greater chance of success.
"This is an issue that we feel very strongly about. As share owners we have a voice and a say and, in this situation, we want to use the levers as fully as possible to ensure the company knows that, as share owners, we expect change. Complacency is not an option.
"By speaking to companies with a unified voice, investors can more effectively communicate their concerns to corporate management.
"The result is typically a more informed and constructive dialogue. There are also benefits from knowledge sharing and efficiency measures from working in a group."
KiwiSaver providers manage more than $50 billion across them which has some clout but, on a global scale, that remains small.
John Berry, chief executive of responsible investment specialist investment firm Pathfinder, believes raising the issue is more important than size.
"Part of it is raising awareness."
Individuals may feel powerless to make change but he pointed to the recent removal of single use plastic bags as a successful result from public pressure.
"People have more power than they think."
He says they can vote in elections, make change with consumer choices, and believes KiwiSaver should also be a place where people can voice their views as well.
"Every dollar we invest in companies should have that aspect as well."
While Milford pulling its investment in Facebook might not have a direct impact on the company's share price, it raises awareness of the issue, Berry said.
"It indirectly changes things by raising awareness and making it something people are going to talk about."
"It challenges Facebook in terms of getting the conversation going around this."
Berry said KiwiSaver was a long-term investment and, as such, should take responsible investment into account.
But that left providers trying to come up with a set of investment values that matched what investors wanted.
The challenge was that people don't all want the same thing, Berry said.
It meant providers offering funds that ranged from investing in any company which was legal to those who decided to only invest in companies that did good.
Berry said it was good to have a variety of offerings in the market as it allowed people to pick the one that suited them best.
But he said providers needed to make it clear what they did and didn't invest in to make it easy for investors.
"People need to understand what is in their KiwiSaver."
And he pointed out that there are many grey areas.
"Tobacco companies and their products are legal but many Kiwis would not want their retirement savings going into them."
Most providers have pulled out of tobacco stocks but one major provider has remained invested until recently.
Berry said the challenge around armament investment was choosing which weapons were okay to invest in and which weren't.
KiwiSaver providers pulled out of investing in companies linked to cluster bombs and nuclear weapons in 2016.
But there are still investments in other companies linked to military grade weapons and then there are the civilian weapon makers and sellers which are in a number of indices. That means they are likely to be held indirectly by a number of KiwiSaver providers.
"It is really complex," said Berry.
The Government is banning the ownership of semi-automatic weapons and military style weapons but has not banned investment in those companies.
What the social media companies are doing
Facebook says it has removed the attacker's original video, which was viewed about 4000 times on the site, within minutes of being contacted by the New Zealand police.
In the 24 hours after the attack, it removed about 300,000 reposted videos and blocked more than 1.2 million attempts to upload it.
"We continue to work around the clock to prevent this content from appearing on our site, using a combination of technology and people," deputy general counsel Chris Sonderby told The Financial Times.
YouTube has removed tens of thousands of videos as well as closing hundreds of accounts that promoted the shooter. "Our teams are continuing to work around the clock to prevent violent and graphic content from spreading, we know there is much more work to do," a spokeswoman said.
Twitter has said it was "continuously monitoring and removing any content that depicts the tragedy" and urged users not to view or share it.