MEXICO CITY — A dispute between Mexico’s government and the nation’s sports federations over how public money is spent and how athletes will be selected for the 2016 Olympics could result in Mexico’s being barred from participating as a team at the Games.

Mexico’s Olympic committee and the national sports commission have traded allegations in recent days as the case heads to the International Olympic Committee, which, if it perceives political meddling, could take the rare step of barring the nation.

Athletes could still compete and march under the I.O.C. banner but would not hear their national anthem at the winners’ podium or otherwise participate as a team. Mexico won seven medals at the London Games in 2012, including a gold in men’s soccer.

Carlos Padilla Becerra, the head of the Mexican Olympic committee, said Friday in an interview that the national commission, known by its Spanish acronym Conade, had in recent months sought closer scrutiny of the federations’ finances and had moved to replace some of the federation managers, even going so far as to draw up lists of athletes who should go to the Games.