The National Football League’s insurers were cleared to begin gathering evidence in their effort to avoid paying the league more than $1 billion in costs for thousands of lawsuits by former players over head injuries.

A New York state judge on Friday said insurers can proceed to collect documents and interview officials and doctors in their case against the NFL. Insurers, including Travelers Cos. and Markel Corp.’s Alterra America Insurance Co., filed lawsuits seeking a ruling that they aren’t obligated to provide coverage.

The NFL had sought to keep the insurers’ suits on hold while it resolved claims covering more than 20,000 retired players who accused the league of negligence and failing to inform them of the link between repeated head trauma and brain injury.

Earlier this month, a federal appeals court in Philadelphia found the $765 million settlement between the NFL and retired players imperfect but fair. About 1 percent of the players opted out of the settlement, and some who objected to the deal asked the appeals court yesterday to review its decision.

The NFL sued more than 30 insurers in California state court in August 2012, accusing them of refusing to pay for the defense of the concussion suits. Insurance companies fired back later that month with their own cases in New York, seeking a declaration that they don’t have to provide coverage. The California case was put on hold pending the outcome of the New York suits.