Meanwhile, the Government has moved to ban offshore oil and gas exploration in New Zealand.
Greenpeace Climate Campaigner Amanda Larsson said the obvious next step for the Government would be to ensure that New Zealand dollars aren't funding the climate crisis through investments in fossil fuel companies, either here or overseas.
"New Zealanders' retirement savings shouldn't be bankrolling industries that directly threaten the future they are saving up for."
The almost 130 companies are from 30 countries with the majority in North America. Some 22 of the companies are from Canada and 43 are from the US.
Just one company, Z Energy, is from New Zealand but the Super Fund's $84 million stake in the company represents the largest of the fund's investment in any oil and gas company in the world.
French company Total SA was second, with $75 million and Canadian-based Enbridge comes in third with just over $50 million.
In Opposition, the Greens campaigned on divesting all of the Super Fund's assets away from fossil fuels.
"The Guardians of the New Zealand Superannuation Fund are betting our money on a climate catastrophe," the Greens' co-leader Russel Norman, who is now the head of Greenpeace, said at the time.
In 2016, the Super Fund had $745 million invested in oil and gas stocks.
Since then, the Fund has sold $500 million worth of oil and gas stocks – the Fund has grown from $30 billion to $41 billion over the same period.
"As at today, if the Fund just 'bought the market', it would hold $1.1 billion in oil and gas stocks," a spokeswoman for the Super Fund said.
Larsson said now that the Greens were part of a Government that is championing climate action at a global level, "it's time to walk the talk".
Although he acknowledged he had also campaigned on this when in Opposition, Shaw said he was happy with the work the fund had done, in terms of its climate change policy.
"Broadly speaking, I'm really pleased with their direction of travel and I think they're doing a whole lot better than the ACC fund or a lot of other funds."
In fact, he said the Super Fund is one of the leading funds around the world in terms of its climate change strategy.
The Super Fund's head of responsible investment Anne-Maree O'Connor said it had approached climate change from "an investment rather than an ethical perspective".
"Our approach is consistent with the transitional approach taken by the Government in its approach to oil and gas domestically. We have reduced the risk in the Fund's portfolio but we also acknowledge that oil and gas will continue to have a role for some time yet."
She pointed out that in 2017, the Super Fund achieved an AAA rating in the Global Climate Index report – which covers 500 of the world's biggest asset owners and rates them in terms of their strategies in responding to climate change.
"We are very comfortable that the targeted approach to divestment that we have taken, in combination with engagement and seeking new investments in renewable energy and transformational infrastructure, is the best way of managing climate change risk to the Fund," O'Connor said.
But Shaw said when looking at the trends around energy stocks it was clear "renewable energy as a category is outperforming fossil fuels and that trend will only continue".
"I think that fund managers in New Zealand and directors of companies that are looking for investment need to do a much better job of assessing the risks they are exposed to and then report on that risk to their shareholders."
National's finance spokeswoman Amy Adams said it is important politicians resist involving themselves in the investment decisions of the Super Fund for the simple reason that politicians do not have the expertise to maximise the return on investment.
"If politicians started directing the Super Fund in its investments then that would ultimately lower returns, reduce the balance of the Super Fund and consequently reduce the capability of the fund to support the future superannuation needs of New Zealanders."
