San Francisco City Attorney Dennis Herrera hit back against the National Rifle Association on Thursday, asking a federal judge to toss out the lawsuit the pro-gun group filed against the city last month that accused the Board of Supervisors of violating its First Amendment rights.

The NRA’s lawsuit came less than a week after the Board of Supervisors passed a resolution labeling the group as a “domestic terrorist organization” for its efforts to block gun reform legislation. Supervisor Catherine Stefani brought the legislation to the board two days after the deadly shooting at the Gilroy Garlic Festival.

In asking the court to dismiss the suit, Herrera’s office argues that the board’s action — a nonbinding resolution — represents an expression of a policy view and not a mandate to take any action.

The NRA claimed in its lawsuit that the resolution would result in a blacklisting of the organization and anyone affiliated with it, potentially chilling their own rights of free expression. The resolution, the NRA claimed, constituted an “implicit censorship regime” by the city.

“Criticizing the NRA is not against the law,” said John Coté, a spokesman for Herrera’s office.

“The NRA is responsible for blocking common-sense gun safety measures like universal background checks, renewing the assault weapons ban and restricting high-capacity magazines,” Coté said. “For that, it should be publicly condemned. Legislators have the same free speech rights as their critics.”

A few weeks ago, Mayor London Breed reminded city staff in a memo that the nonbinding resolution does not limit contracts with groups doing business with the pro-Second Amendment organization.

“I knew all along that this was a non-binding resolution,” Stefani said in a statement on Oct. 1 and reiterated Thursday. “We made our point: the NRA is a terrorist organization. I will keep fighting them using every tool at my disposal.”

The NRA said Thursday it won't withdraw its lawsuit yet.

“The NRA will pursue this case until the City of San Francisco officially withdraws its unconstitutional threat and makes amends for the harm suffered by the NRA, its members, and its supporters,” NRA attorney William Brewer, said in an email. “The memo previously issued by the mayor underscores the merit of the NRA’s claims — but does not adequately address the negative impacts of the city’s unconstitutional resolution.”

Dominic Fracassa is a San Francisco Chronicle staff writer. Email: dfracassa@sfchronicle.com Twitter: @dominicfracassa