A string of artificial-intelligence safety incidents is exposing a gaping hole for the fast-growing industry: the lack of available insurance.

Rogue agents have hacked into websites. AI chatbots have been accused of encouraging suicides and murders. An agent submitted fake unsolved murder tips. The latest episodes add to existing lawsuits AI companies face alleging chatbot harm and copyright violations when models are trained.

The seemingly limitless possibilities of artificial intelligence to change the world also include a wide-ranging capacity for harm that could leave companies that produce or use AI legally vulnerable.

The biggest AI companies are racking up potential legal liabilities running into the tens—if not hundreds—of billions of dollars, as AI adoption spreads through the economy, according to insurers specializing in AI risks. Some industry officials have even called for the U.S. government to provide a liability backstop.

AI companies have the usual corporate suite of traditional insurance policies, such as general liability and cyber-insurance, brokers said. But the industry’s phenomenal rate of growth means AI-related claims have the potential to outpace the limits on that coverage, according to AI and insurance industry insiders.

“There’s too little capacity in every aspect of the risk that is being created by the AI capital boom,” said Nick Studer, chief executive of Marsh Risk, the insurance brokerage arm of professional-services firm Marsh. “But that is changing.”A few insurers sell coverage specifically for AI risks, including from agents. But the policy limits are small compared with the potential exposure of the AI giants. Reinsurer Munich Re offers a policy to cover errors by AI models with limits of up to $50 million, according to a spokesman.

Startups are hoping to fill the gap, and insurance companies more broadly see AI down the road as a new opportunity for offering specialty products.

Rune Kvist, a former Anthropic employee, is a co-founder of the Artificial Intelligence Underwriting Company, which has backing from Lloyd’s of London’s insurance marketplace.

The planned IPOs of Anthropic and OpenAI are adding to the focus on the “gaps in the insurance and other safety nets for those risks,” says Kvist.

The biggest AI companies are willing to buy billions of dollars of coverage and have the balance sheet and cash to afford it, said George Lewin-Smith, chief executive of Testudo, a U.K.-based AI insurer also affiliated with Lloyd’s. He added that coverage at that scale for such liabilities isn’t available. “The reality is—it just doesn’t exist on planet Earth,” he said.

AI startups might be exposed to liabilities in ways previous generations of tech companies weren’t. Web portals and social-media companies were largely shielded from being held liable for content on their platforms by a provision of federal law passed in 1996 known as Section 230.

The protection may not be as useful for AI companies because they materially contribute to the content, according to a report by Moody’s Analytics.

The biggest AI developers have deep enough pockets to cover many liabilities. But a major incident that causes widespread economic or human harm could swamp a company’s financial buffers.

Insurance firms are selling specialty policies to the major AI companies as a way to reassure nervous regulators and investors.

A policy, even for far less than the potential loss, demonstrates that an outside party has assessed and is willing to cover a risk. Policies for AI risks are often underwritten on the basis of simulation testing of the likelihood of errors, creating a de facto audit of the underlying tech.

Insurance—or the inability to acquire it at an affordable price—has the potential to help police AI by imposing guardrails on both developers and users as a condition of coverage, brokers and insurers say.

Venture capitalist David Sacks, part of a new White House task force on AI, suggested insurance could add teeth to a voluntary industry agreement on controls. In a social-media post, he said a safety issue reported internally under the agreement could in some circumstances be used by an insurer to deny directors-and-officers coverage—protection designed to shield executives from personal liability.

Insurers are divided over how best to respond to the spiraling risks—and opportunities—from AI. The industry is racing to profit from AI data centers, described by broker Aon as “the insurance market’s biggest ever opportunity.”But the industry is increasingly worried about so-called silent risk, where mainstream policies for businesses using AI neither affirmatively cover nor exclude losses caused by the technology. More than 90% of AI risks covered by insurance fall into this silent category, according to Aon.

AI losses don’t fit neatly into existing insurance categories, creating scope for disputes about what is and isn’t covered, according to a report this year by Rand, a U.S.-based think tank. The report flagged an “emerging mismatch between rapid enterprise adoption of AI and the fragmented market for insuring (or not insuring) AI use, particularly in the United States.”The different types of AI-inspired losses range from bodily injury and property damage—caused by, say, an error-prone factory robot—to copyright infringement, unauthorized data disclosures, hallucinated errors and regulatory penalties.

An option to exclude AI from companies’ general liability and other policies is spreading through the industry.

Verisk’s Insurance Services Office, which provides widely used standardized insurance policy forms, this year introduced optional exclusions for generative AI. It is weighing additional optional exclusions for other AI-related exposures, including agentic AI, according to a Verisk spokeswoman.

American International Group and Chubb are among a growing band of insurers with the option to use the existing Verisk exclusions, should they want to do so in the future. An AIG spokesman said the insurer automatically adopts the standardized forms, which is a “common practice across the industry.”Marsh, the biggest global insurance broker, which acts on behalf of companies negotiating with insurers, this month sounded the alarm on exclusions. Studer, the head of its insurance brokerage, said in a letter to leading insurers that excluding AI risks would be a “backward step” for the industry.

“It will increase coverage uncertainty and increase disputes,” Studer wrote, according to a copy of the letter reviewed by The Wall Street Journal.

Marsh will recommend that clients seek cover elsewhere if an insurer imposes AI exclusions, the letter said. But it added that brokers, insurers and clients will need to work together to manage “genuinely novel exposures…around agentic AI and autonomous decision-making.”

Write to Jean Eaglesham at Jean. Eaglesham@wsj.com