(CNN) A lawsuit filed by the National Rifle Association says the gun advocacy organization will have to close its headquarters, shut down its online media presence and stop holding rallies and conventions if it is stymied by New York state from doing business with banks and insurers.

The NRA suit, filed in May and amended in July, says New York Gov. Andrew Cuomo is trying illegally to coerce financial companies into halting business relations with the group.

"Far from protected government speech, defendants' actions constitute an 'implied threat to employ coercive state power' against entities doing business with the NRA," the lawsuit says, employing a quote from a 2003 free speech case.

The NRA lost its insurance coverage from its provider in February when an entity of Lockton Companies dropped the organization.

"Lockton Affinity has notified the NRA that it will discontinue providing brokerage services for NRA-endorsed insurance programs under the terms of its contract," the insurance giant tweeted on February 26.

The NRA said it had spoken to other insurers to get corporate coverage, but said "nearly every carrier has indicated that it fears transacting with the NRA" in light of actions by New York authorities.

The organization is suing Cuomo, the state Department of Financial Services, and DFS Superintendent Maria Vullo.

"New York, we will not be intimidated by the NRA's frivolous lawsuit to advance its dangerous gun-peddling agenda," Cuomo has said.

Friday, he announced the state had filed a motion to dismiss the case. A hearing is scheduled for September 10.

In commenting about the NRA's financial claims in the updated version of the lawsuit, the governor said: "If I could have put the NRA out of business, I would have done it 20 years ago."

A lawyer for the NRA said Friday that New York officials are unfairly targeting First Amendment rights.

"We believe the filing is a misguided attempt to deflect from the fact that defendants overstepped their legal and regulatory authority -- to the detriment of the Constitution and New York insurance consumers," William A. Brewer III said.

The NRA alleges in its claim that it has incurred tens of millions of dollars in damages because of the defendants' actions. It says that the organization's access to banking services are "imperiled."

Lawsuit followed insurers being fined

The lawsuit, when it was originally filed in the US District Court for Northern New York, came days after the Department of Financial Services fined several insurance companies hundreds of thousands of dollars for participating in an NRA-backed liability insurance program for gun owners.

The state also secured agreements from those companies not to offer such insurance again.

The suit contends that what the state has done "prevents, or at a minimum, chills," the First Amendment rights of the NRA and its members to free speech -- including their right to speak freely about gun-related issues.

The suit alleges this amounts to a "blacklisting campaign (that) will continue to damage the NRA and its members" if the court doesn't act.

The Fairfax, Virginia-based NRA says it will not be able to function without access to banking services, which it needs to process gifts and other revenues as well as make payments.

"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," the court document says.

State urged banks, insurers to review NRA relationships

The claim also points to an April news release in which Cuomo called on the DFS to urge insurers and banks in New York "to review any relationships they may have with the National Rifle Association."

The release noted that a number of companies were ending relationships with the NRA -- including by ending special discounts or other special services for NRA members -- after February's shooting at a high school in Parkland, Florida, that left 17 dead.

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In that same release, Vullo urged "all insurance companies and banks doing business in New York to join the companies that have already discontinued their arrangements with the NRA."

Vullo also sent letters to banks and insurers asking them to review any relationships with the gun lobby organization.

Focus on 'Carry Guard' insurance program

The lawsuit partly focuses on the state's crackdown on the NRA-branded "Carry Guard" program, which provides liability insurance for policyholders involved in shooting incidents.

The DFS has said the program violated state insurance law. It has argued the NRA publicized the program as something it created -- and the DFS asserts the NRA doesn't have a license to conduct insurance business in New York.

In early May, the DFS fined two insurers involved in the Carry Guard program.

The DFS said insurer Lockton Caos. LLC and its affiliate, Lockton Affinity LLC, agreed to pay a $7 million fine for administering the program.

Five days later, the DFS said insurer Chubb Ltd. and its subsidiary, Illinois Union Insurance Co., agreed to pay $1.3 million for underwriting the program.