Religious groups have urged Pope Francis to back a campaign to encourage millions of people, organisations and investors to pull their money out of the fossil fuel industry.

Multi-faith groups in Australia and North America have sent a letter to the pope saying it is "immoral" to profit from fossil fuels.

The letter, shown exclusively to the Guardian, says 80% of global fossil fuel reserves must "stay in the ground" if dangerous climate change is to be avoided.

"We urge you, as a person held in high esteem by many millions around the world, to speak clearly about the place of divestment from fossil fuels as one significant means to avert the worst of climate disruption," the letter says.

"You could have a desperately needed influence on the direction humanity takes from here. We urge you to use this influence."

The plea to the Vatican follows a call from archbishop Desmond Tutu for an anti-apartheid style boycott of the fossil fuel industry. Writing in the Guardian last week he said, "People of conscience need to break their ties with corporations financing the injustice of climate change."

The letter sent to the pope's offices in February is co-signed by the Australian Religious Response to Climate Change (ARRCC) and US-based GreenFaith.

Thea Ormerod, chair of ARRCC and a practising Catholic, said: "If the extracting and burning continues, the world's children and grandchildren may have little or no chance of any kind of decent life on this planet, particularly those who live in the global south.

"For corporate bodies to continue seeking to profit from extracting coal, oil and gas in spite of this fact, is institutionalised greed, selfishness and arrogance. I believe as a Catholic that it is sinful."

Both ARRCC and GreenFaith are umbrella organisations working mainly with Christian, Hindu, Muslim, Buddhist and Jewish groups.

The letter was also signed by a New Zealand campaign that has seen five Anglican dioceses pledging to divest from fossil fuels.

GreenFaith executive director, the Rev Fletcher Harper, said: "Pope Francis's support would provide a powerful validation of the moral rightness of divestment and reinvestment in response to the climate crisis, and would immediately signal the need for dramatic action. It would be of vital significance."

Bill McKibben, the US environmentalist and one of the leaders of the divestment campaign, said: "For people of faith, it's become clear that we can't fulfill the commandment to love our neighbors without breaking the fossil fuel addiction.

"That's why so many churches have been divesting from the richest companies on earth. After all, where your treasure is, there is your heart as well."

Scores of religious groups, educational institutions, philanthropic foundations and cities have pledged to go "fossil free", while others, such as Harvard University, have pushed back against requests.

Last September the White House announced it had joined Denmark, Finland, Iceland, Norway, and Sweden "in ending public financing for new coal-fired power plants overseas, except in rare circumstances."

That followed the US Export-Import Bank tightening its rules on lending to foreign coal-power projects in an attempt to cut greenhouse gas emissions. The World Bank has introduced similar restrictions on its lending.

The Norwegian government is reviewing its US$838bn sovereign wealth fund, ranked the largest in the world, to consider stopping fossil fuel investments.

In response to moves in Norway, the World Coal Association has said major coal companies who were the potential targets for divestment were also spending money on so-called "clean coal" technologies.

The association said divesting coal assets would not cut demand for the fuel, ignored its contribution to economic development and would "do nothing" to address climate change.

The letter to the pope was sent a week before Australia's Cardinal George Pell was appointed to an influential senior position within the Catholic church and the Vatican as the head of a new secretariat for the economy.

Cardinal Pell has expressed extreme scepticism of the science linking greenhouse gas emissions to climate change.

In 2011 he delivered the annual lecture of the UK's sceptic group the Global Warming Policy Foundation, founded by Lord Nigel Lawson, and claimed carbon dioxide was "not a pollutant" and animals would not notice a doubling of atmospheric CO2.

He said climate change campaigners were following a "mythology" which he said was attractive to the "religionless and spiritually rootless".

The Vatican declined to comment on the letter.