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On the very day last week when Norway’s parliament discussed banning its sovereign wealth fund from investing in coal miners, Store Norske, the country’s state-owned coal miner, opened a mine on the Arctic island of Svalbard. Hypocrisy was the word on the lips of environmentalists.

Now that charge has gained even more resonance. In the early hours of Friday, the two governing centre-right parties in Norway and two of their allies killed off the plans for an immediate ban on coal investment. Instead, they agreed something far more ambitious. An expert group will be set up to see whether Norway’s oil fund – the world’s largest sovereign wealth fund with assets of $840bn – should stop investing in any companies related to fossil fuels – not just coal, but oil and gas, too.

The paradox was not lost on observers: the so-called oil fund (its official name is the Government Pension Fund Global, despite it having no pension liabilities) receives all its money from Norway’s oil and gas reserves. Can it make sense for a fund financed solely by petroleum to be banned from investing in petroleum assets because they are deemed unsustainable?

The accusation of hypocrisy clearly makes the managers of the oil fund uneasy. Yngve Slyngstad, the fund’s chief executive, says it can deal with any mandate politicians give it on behalf of the fund’s ultimate owners: the Norwegian people.

But his overseer, head of the central bank Øystein Olsen, says any decision to exclude a big group of companies from its investment portfolio – oil and gas companies account for 8.4 per cent of the fund’s equities holdings – is likely to hurt both returns and risk.

A broader concern, only uttered privately, is that such a ban could lead to the fund being viewed abroad as a political object. The oil fund has carefully cultivated its image as a serious financial investor. There has, for instance, been no overt criticism of western central banks’ policy of quantitative easing despite deep unease inside the fund over what it means for bond investors.

But former fund officials say one of the big worries internally is that the fund could get caught up in a political fight abroad if it is seen as an arm of Norwegian state, possibly even having its assets expropriated.

Such jitters are increasing as the fund grows rapidly. It now owns on average 2.5 per cent of every listed company in Europe and 1.4 per cent of every company in emerging markets.

But Norwegian politicians are quick to cite this vast size – the fund is forecast to have $1.2tn of assets by 2020 – to justify taking an increasingly active approach to ownership. Responding to the charges of hypocrisy, Svein Flåtten, an MP in the ruling Conservative party and its financial spokesman, says: “The fund is large, so is our responsibility.”

“I think that a fund like ours always should have a responsibility to consider and discuss the consequences of investments on not only the environment and possible climate change, but also on other ethical questions,” he adds. “This proposal [to potentially ban fossil fuel investments] is a step in that work.”

The charge of double standards is not limited to the oil fund. Norway likes to tout itself as green, with most of its power coming from hydroelectric sources, while the best-selling cars recently were Tesla’s Model S and the Nissan Leaf, both electric.

At the same time, however, its emissions per capita are some of the highest in the world thanks to its oil and gas production. Environmentalists say the only real way to cut emissions meaningfully is to leave some of the oil in the ground, but few politicians have endorsed that.

The oil fund has been hugely successful in its goal of preserving Norway’s petroleum wealth for future generations. But as it grows in size, so the dilemmas multiply. Is it too big? Should it invest in riskier assets? How can it be a responsible owner?

Even inside the fund, there seems to be a realisation that it can no longer pretend to be purely a financial investor with no bigger responsibility. The question now for Norway is whether it can head off the perception of acting under double standards even as it tries to be an ethical investor.