A fossil fuel firm is suing its insurer for refusing to cover a climate lawsuit in a case that could affect the wider industry’s ability to defend itself from litigation.

Aloha Petroleum, a subsidiary of the US-based Sunoco, filed a claim against AIG’s National Union Fire Insurance Company of Pittsburgh earlier this month, arguing it had failed to protect Aloha from the mounting costs of defending climate-related claims by local governments in Hawaii.

According to documents filed in the latest lawsuit, Aloha has already incurred more than $880,000 (£750,000) in defence costs, and expects these to grow significantly as litigation progresses. Its insurance company will not pay out.

The lawsuit follows another, filed by the insurance company Everest in June, which is asking Massachusetts superior court to make a similar decision about whether coverage can be denied to Gulf Oil.

These are some of the first disputes over insurance coverage for climate crisis litigation to be heard in the courts. Both insurance companies say climate litigation is covered by exclusions for “pollution” in their clients’ general liability policies. If they succeed, the fossil fuel firms could be on the hook for millions of dollars in legal fees, in addition to any future damages awarded in court.

The only previous decision on this subject was in 2012, when the Virginia supreme court ruled that Steadfast insurance company had no duty to cover the energy firm AES Corporation in a climate lawsuit brought by the Native American village of Kivalina. The Kivalina lawsuit was unsuccessful, but in the US that usually still leaves defendants liable for their legal costs.

Russell Butland, a senior associate at law firm Allen & Overy who advises companies on commercial disputes, said the extent to which the latest lawsuits set a precedent for future claims would depend on the specific wording of insurance policies and the relevant laws in particular places.

“However, exclusions for pollution risks are a common feature of all types of insurance, and therefore the outcome will be of real interest to all companies and individual directors seeking to manage their risks for similar litigation,” he said.

The world’s biggest greenhouse gas emitters are increasingly being targeted by litigation challenging their inaction on the climate emergency and attempts to spread misinformation.

The lawsuits underlying Aloha’s claim were brought by local governments in Hawaii against companies including Sunoco, ExxonMobil and Shell. Honolulu’s case alleges the big oil firms “engaged in a coordinated, multifront effort” to deny the threat posed by global heating, to discredit the science of the climate crisis, and to deceive the public “about the reality and consequences of the impacts of their fossil fuel pollution”.

It was also one of a swathe of lawsuits given the go-ahead to be heard in a state court this year; the latest such ruling was made earlier this month in Delaware.

Jason Reeves, ta partner in the London office of the law firm Zelle, said this was important because plaintiffs were more likely to succeed on their claims than in federal court and to obtain hefty judgments. Even if judgments were years away, the costs of defending the case could be high.

“You will see a continued escalation of ‘parallel’ climate litigation cases between policyholders and their insurers as policyholders present claims in relation to defending these lawsuits,” he said.

It is not only a risk for the fossil fuel industry. Mary Sweeters, a senior strategist for the Insure Our Future campaign, said insurers underwriting the polluters that were subject to climate litigation may face significant losses.

Last year, the UN Environment Programme concluded that insurance firms were not assessing the risk of climate litigation in a rigorous way, largely because they had not yet paid out for any claims. This was echoed in the Bank of England’s first climate stress test earlier this year, which considered the growing prospect of climate-related payouts – in particular in lawsuits against company directors – and found that not all insurance companies had properly considered how this would affect their business. Nor are companies preparing properly for increasing claims for the impactsof extreme weather events.

However, parts of the insurance industry are waking up. Some companies are now asking clients about their climate crisis reporting while negotiating liability coverage or providing more insurance capacity to those with high ESG (environmental, social and governance) ratings.

The Lloyd’s Market Association has also published a model clause for liability policies that excludes cover for climate litigation, which insurers can use in their own documentation. Reeves said these kinds of exclusions were likely to become more common.

They would not protect companies in cases such as that of Aloha Petroleum, however, where the insurance policies in question dated back to the 1980s.

None of the insurers or fossil fuel companies involved in the latest lawsuits responded to the Guardian’s request for comment. But, in its latest ESG report, AIG recognised that climate lawsuits had increased in recent years. “While these kinds of actions have not resulted in material losses, AIG continues to assess the evolving norms for disclosure and expectations for corporate action around climate change, which create the potential for more climate-related litigation.”

Sweeters said lawsuits such as those brought by Aloha were an indicator that pressure was mounting on insurers for underwriting fossil fuel projects.

Earlier this year, AIG announced it would no longer insure new coal-fired power plants, thermal coalmines or oil sands. Sweeters said industry leaders were starting to act by restricting their portfolios – but “by and large, the industry falls far short of where it needs to be”.