The fossil fuel industry was deeply “unsettled” by comments from energy secretary Ed Davey raising the prospect that their assets could be rendered worthless by global action on climate change, according to a letter of protest sent to the secretary of state.

Malcolm Webb, chief executive of Oil and Gas UK, which represents the industry, wrote to Davey saying he was “perplexed” by the “conflicting and confusing messages” and accused him of making investment in the North Sea less attractive. The letter was released to the Guardian under freedom of information rules.

The issue was also raised by Erik Bonino, chairman of Shell UK, at a meeting with Davey in January, at which Bonino said if Shell “knew there were to be no more fossil fuels, [it] could cash out and give shareholders their money back in four years”.

The strong reactions reveal the depth of concern inside fossil fuel companies at analyses showing there are already three times more fossil fuels in proven reserves than can be burned if global warming is to be limited to 2C, the pledge made by the world’s nations. If a global climate deal makes good on that pledge, those coal, oil and gas reserves could become worthless, potentially losing investors trillions of dollars. Fossil fuel companies, which spent $650bn (£422bn) in 2013, searching for more reserves are also under attack from a fast-growing divestment campaign, which has persuaded over 180 groups to dump their fossil fuel stocks.

Davey made the comments at the UN’s climate change summit in Lima in December, saying that some analysts estimated that the action needed to cut carbon emissions and tackle climate change could result in the global fossil fuel industry losing as much as $28tn (£18tn) in the next 20 years. Davey said he supported calls for asset managers and banks to disclose the size of their fossil fuel holdings to investors. “There is a case for making it mandatory,” he said. “People need to know the risks.”

Webb wrote to Davey a few days later: “[Newspaper] articles reported you backing moves that would encourage investors to think about moving their money out of ‘risky’ fossil fuel assets, suggesting global emissions limits could make hydrocarbon reserves unburnable, therefore stranding assets and rendering them worthless.”

Webb said: “I must confess I find these statements unsettling. They come, after all, at a time when you and the Treasury are putting great effort into delivering the much-needed regulatory and fiscal reforms that will make the UK North Sea more [original italics] attractive to investors in oil and gas, not less. I am intrigued to understand how such opposing viewpoints can be reconciled.”

Webb also cited the tax breaks promised by chancellor George Osborne in December’s autumn statement as testament to “the crucial need to stimulate new investment in offshore oil and gas development that will safeguard UK jobs, tax revenues, exports and secure primary energy supplies. Yet still we see conflicting and confusing messages coming out of the Department of Energy and Climate Change.”

Davey said in a reply: “My recent comments were about highlighting that moving to a low-carbon economy is a ‘business smart’ choice, both in terms of risks and returns. I simply reflected what a number of other organisations have been promoting about sounding a note of caution internationally on the need to carefully consider fossil fuel investment in the light of their life-cycle carbon emissions.”

Davey cited the statement by Mark Carney, governor of the Bank of England, that the bank is deepening and widening its enquiry into stranded assets and whether they pose a risk to the nation’s financial stability. He also cited the decision of the heirs to the Rockefeller oil fortune to sell all the fossil fuel holdings in their $862m portfolio. In 2014, the president of the World Bank, Jim Yong Kim, said: “Sooner rather than later, [financial regulators] must address the systemic risk associated with carbon-intensive activities in their economies.”

Davey said he “fully recognised” that the world would need oil and gas for decades to come. “The challenge we face is to effectively address climate change while at the same time ensuring that we remain energy secure and promoting economic growth. As government, we are clear these key priorities are compatible,” he wrote, adding “we have put in place policies needed to maximise the recovery of oil and gas from the UK continental shelf.”

In a handwritten postscript, Davey said: “Indeed my comments were focused far more on coal than oil and gas. This has been a consistent theme of mine! Happy to pick up at our next meeting.”

The note of the meeting between Davey and Shell’s Bonino states: “Davey’s purported comments in Lima were discussed, with Bonino commenting that he knows the SoS was ‘wildly misquoted’.” Davey is not recorded as agreeing. “Davey commented that he had said that investors need full disclosure so they can take a decision,” the note recorded.

James Leaton, research director at think tank Carbon Tracker, which has led the analysis of stranded fossil fuel assets, said: “It is disappointing that Oil and Gas UK seems confused about how to rationalise tackling climate change and developing more oil and gas. Unfortunately this reflects the ongoing contradiction in many oil company positions that they want to increase oil production despite the importance of preventing dangerous levels of warming.”

Leaton said: “Shell have admitted that a third of their projects are not making any return for shareholders. From a financial sense for investors expecting a return, those assets look pretty stranded. Carbon Tracker’s focus is to make sure more capital is not sunk on high-cost, high-carbon projects, like Kashagan in the Caspian or oil sands in Canada.”

In January, Shell made the unusual move of backing a climate proposal from a group of activist shareholders. The resolution, which will be voted on at Shell’s AGM in May, requires the oil major to test whether its business model is compatible with the pledge by the world’s nations to limit global warming. Also in January, a scientific analysis published in Nature concluded that 80% of coal reserves, 50% of gas reserves and 33% of oil reserves were unburnable if warming is to be limited to 2C.

Letter from Malcom Webb

Response from energy secretary Ed Davey.