NEW YORK (Reuters) - Several subsidiaries of Travelers Companies Inc sued the National Football League and a host of other insurers, seeking to avoid paying to defend the league against a wave of brain injury-related claims by thousands of former players and their families.

The lawsuit was filed on Tuesday in New York State Supreme Court, one week after the NFL sued three dozen insurance companies in an effort to force them to cover the costs of defending the claims.

According to the Travelers lawsuit, the company provided liability coverage for NFL Properties, the league’s merchandising arm, but not the NFL and should not be required to pay for a joint defense. The insurer points out that a “master complaint” filed jointly by some 2,000 former players in June alleges 14 counts against the league, but only two against NFL Properties.

“Travelers is not required to pay any defense costs of the NFL with respect to the underlying lawsuits,” Travelers said in its lawsuit.

The insurance companies sued by the NFL and named as defendants in the Travelers lawsuit provided coverage to the NFL or one of its affiliates sometime between the 1960s and today.

“Last week, the NFL filed a comprehensive lawsuit in California against 32 insurers to ensure an orderly and comprehensive determination of its insurance rights and its carriers’ obligations,” NFL spokesman Greg Aiello said. “This new filing by Travelers does not alter our objectives.”

The NFL is facing a growing number of claims from former players who say football left them with debilitating brain injuries. Some of the lawsuits accuse the league of deliberately hiding known injury risks to profit from the game’s hard-hitting style, a charge the NFL has rejected.

Several retired NFL players have committed suicide in recent years by shooting themselves in the chest, in some cases with the explicit goal of preserving their brains for study.

The case is Discover Property & Casualty Co. et al. vs. National Football League et al., New York State Supreme Court, New York County, No. 652933/2012.