The long-running battle between Gov. Andrew M. Cuomo of New York and the National Rifle Association, which says it has lost millions of dollars because of state officials’ political agenda, entered another round of legal wrangling and public posturing this week.

Mr. Cuomo announced on Friday that the state was moving to dismiss a lawsuit the N.R.A. filed in federal court in May, which he called “frivolous.” The lawsuit, which accused state officials of “blacklisting” the gun rights organization, was amended with sharper language last month.

At issue is whether New York regulators violated the constitutional rights of the N.R.A. by preventing financial institutions and insurers in the state from doing business with the organization.

In the lawsuit, the N.R.A. accused Mr. Cuomo, as well as the New York State Department of Financial Services and its superintendent, Maria T. Vullo, of discrimination that violated the organization’s right to free speech.