NEW YORK — NFL commissioner Roger Goodell reassured retired players that their pensions and disability benefits would not be reduced in a labor dispute next year, refuting statements made by the NFL Players Association.

In a letter to the NFL Alumni Board of Directors on Wednesday, Goodell wrote that claims made by the union — including NFLPA executive director DeMaurice Smith — that retired players have the potential to be affected next year ‘‘have no basis in fact.’’

‘‘In all my conversations with DeMaurice Smith, he has never raised the subject with me,’’ Goodell wrote in response to questions raised by NFL Alumni board members. ‘‘Had he done so, my answer would have been unequivocal — there will be no reduction in pension or disability payments to retired players during 2010.’’

In a statement released by the NFLPA, Smith responded by challenging the NFL to guarantee paying benefits beyond 2010.

‘‘If these benefits are now being guaranteed for one year by the NFL, which they currently are not, then that’s a win for the players,’’ NFLPA benefits director Miki Yaras-Davis said.

Portions of Goodell’s letter were released by NFL Alumni and Fourth and Goal, an independent retired-player advocacy group. Goodell was responding to concerns raised by the groups’ directors after NFLPA members stated retired players would take a hit in an uncapped year.