Local media had reported that FBI agents detained Tapia and Toviggino at New York's JFK Airport on Monday morning before they boarded a charter flight carrying the Argentina squad after the World Cup final, and requested Tapia's devices.
Media outlet Infobae reported US authorities are investigating more than $300 million in AFA-linked commercial contracts, amid wider scrutiny of Argentine football finances following December raids in a money-laundering probe.
According to a witness at the airport, as the Argentine team prepared to board its flight, federal agents questioned both Tapia and Toviggino for about 30 minutes aboard a bus parked on the tarmac.
The association did not name the third party summoned by US courts, but stressed that US authorities had not targeted either Tapia or Toviggino.
"It is absolutely false to claim that Claudio Tapia or Pablo Toviggino have been summoned to testify by the United States justice system. It is also false to claim that their cell phones or any other electronic devices have been seized," the association said in a statement.
"The document in question does not impose any personal measure on the President of the AFA or its Treasurer, does not order their appearance, does not impose any procedural obligation on them, and does not record any seizure or confiscation of property belonging to them."