A group of United States senators sent N.F.L. Commissioner Roger Goodell a letter Tuesday expressing continued concern over what they consider the exclusionary nature of showing select games on the NFL Network.

The letter, obtained by The New York Times, was signed by 13 senators, including Patrick Leahy, a Democrat from Vermont and the chairman of the Senate Judiciary Committee, and Arlen Specter, a Republican from Pennsylvania who has criticized Mr. Goodell on numerous issues, including the New England Patriots’ spying case.

The NFL Network begins its slate of Thursday night games on Nov. 6. The Jets play the Patriots on Thursday, Nov. 13, in a game that will be televised on the NFL Network and on Channel 11 in the New York metropolitan area.

Senator Specter has repeatedly called for the N.F.L. to make its games available to as many viewers as possible on free television, rather than favoring its own cable network.