New York Gov. Andrew Cuomo says he’s discovered a way to kneecap the NRA by outlawing its gun-liability insurance program and is urging other states to follow his lead, saying they have a chance to exploit the gun-rights group’s admitted dire financial situation.

Mr. Cuomo said the National Rifle Association let on in court papers last month how much it relies on the liability insurance program to bolster its bottom line, and could succumb to pressure.

“I believe this insurance product is going to be illegal from a public policy point of view in most states,” Mr. Cuomosaid on MSNBC. “Now that the NRA has said this is a major source of revenue, I’m going to pursue it nationwide.”

The liability insurance, Carry Guard, covers damages and court costs associated with defending against civil or criminal accusations of misuse of a firearm.

But under pressure from New York, which warned of “reputational risks” of doing business with the NRA, some insurers have backed away from underwriting the program.

In May, the state slapped $1 million-plus fines on insurance companies Lockton Cos. and Chubb Ltd., saying they violated state law by marketing and underwriting Carry Guard policies and that the policy improperly provided coverage for criminal proceedings arising from the use of a gun.

The NRA says Mr. Cuomo is engaged in a “blacklisting” campaign to smear the organization, and said its insurance is still available in the rest of the country.

But the gun-rights group also warned in court papers of a chilling effect, saying it has had “serious difficulties” obtaining new corporate insurance coverage and could have to close its affiliated television network if it can’t find a replacement.

“If the NRA is unable to collect donations from its members, safeguard the assets endowed to it, apply its funds to cover media buys and other expenses integral to its political speech, and obtain basic corporate insurance coverage, it will be unable to exist as a not-for-profit or pursue its advocacy mission,” according to an amended complaint filed late last month.

The NRA has sued to stop what it calls Mr. Cuomo’s campaign of harassment.

“The governor’s current campaign against the NRA extends far beyond Carry Guard,” said William A. Brewer III, lead counsel for the NRA in the case. “His scorched earth tactics are designed to prohibit the NRA from having access to insurance and banking services — simply because he disagrees with the political viewpoint of this law-abiding organization.”

The state had launched an investigation in October 2017 into the program, prompting Lockton and Chubb to suspend their participation in Carry Guard the following month.

Lockton issued about 680 Carry Guard insurance policies to New York residents between April and November 2017, some of which were underwritten by Chubb, according to consent decrees announced in May.

The companies agreed in May to pay fines of $7 million and $1.3 million respectively and not participate in Carry Guard or other similar programs in New York, after taking steps months earlier to distance themselves from the NRA.

New York has moved to dismiss the NRA lawsuit, arguing its actions were reasonable steps to prevent a business from assisting criminal behavior.

Mr. Cuomo on Monday said the NRA is made up of “bad guys” and that the group has given a new opening to gun control activists by admitting how big an effect the insurance difficulties could have on the organization’s future.

“If they have less money to bully and threaten politicians into irrational positions I’m not going to lose any sleep over that,” Mr. Cuomo said. “And if they went away, you know, I would offer my thoughts and prayers just like they do every time we have another situation of innocents losing their lives.”

It would be in the NRA’s interest to exaggerate the financial effects of Mr. Cuomo’s moves — but such insurance programs are still a clear moneymaker for gun rights groups, said Robert J. Spitzer, a professor at SUNY Cortland.

“I think they are in financial trouble,” said Mr. Spitzer, who has written extensively on the politics of gun control. “Whether they’re going to be run out of business because of this move by Cuomo not so sure about that.”

Gun control advocates, meanwhile, have cheered the recent reports about the NRA’s supposed financial troubles, saying it’s a sign that their post-Parkland advocacy is working.

“Following the national March for Our Lives and more than 400 sibling marches across the country, and due to the tireless activism of students, gun violence survivors, and Moms Demand Action volunteers, a wave of corporations publicly distanced themselves from the NRA and its dangerous policies,” a spokeswoman for the group Everytown for Gun Safety said in a memo released Monday.