Friends of the Earth Scotland (FoES) says Falkirk is among 20 councils in Scotland that has declared a climate emergency but continues to invest in oil and gas companies.
The campaigners are urging Falkirk to divest investments such as £13.7 million in Royal Dutch Shell - the co-owner along with Exxon of the Mossmorran plants in Fife, Scotland’s third largest climate polluter.
However, a spokesperson for the council says the committee believes it can use its position as an investor to apply pressure to such companies to drive change.
They said: "Both Shell and Exxon Mobil are companies that our investment managers are engaging with.
"Shareholder pressure has resulted in Shell adopting a net zero by 2050 strategy, whilst for Exxon Mobil, in recognition of the need for improvement, our managers have voted against the re-election of the Chair of their Board."
Falkirk Council's pension fund administers the pensions of about 35,000 local public employees including employees of Stirling and Clackmannanshire Councils and the Scottish Environment Protection Agency (SEPA).
FoES has previously criticised Falkirk Council for investing in fossil fuels, after the value of its pensions fell by £34 million recently as stocks in oil and gas fell.
Now, campaigners want the fund to tackle the climate emergency by divesting from fossil fuels ahead of the UN Climate Conference in Glasgow this autumn.
Angus Maclean from Friends of the Earth Falkirk said: “We have been calling for an end to fossil fuels investments and instead a commitment to renewable energy and needed infrastructure like social housing."
"It is time the Falkirk Pension Fund listens and works towards a more sustainable future for all of us.”
A Falkirk Pension Fund spokesperson responded: “The Fund takes its duties as a responsible investor very seriously.
“We own several assets in the renewables sector, including wind and solar farms, and are very much strong advocates of companies taking action to be more carbon efficient.
“We do not think that the issue of global decarbonisation can be solved simply by divesting from a small number of fossil fuel companies.
"Instead, our approach is to engage meaningfully with the companies we invest in.
"Where progress towards carbon efficiency is inadequate, we will ultimately divest due to the risks to our capital.”
“We are also members of several lobby groups all committed to seeking a ‘Just transition’ and in recent years have co‐filed climate change resolutions at BP and Barclays AGMs – the latter leading directly to Barclays unveiling their 2050 net zero ambition.
“Whilst supportive of many climate related initiatives, we do need to bear in mind that our primary (and legal) responsibility is to manage the Pension Fund for the benefit of our stakeholders and that includes taking a balanced approach in order to generate income the £80m of benefits which are due each year.
“As a Fund we remain strongly supportive of principles laid out in the Paris Agreement and look forward to these being consolidated in Glasgow at the COP26 meeting later this year.”