The 44-year-old Italian was asked on several occasions about his beliefs and whether he supported fascism but dodged the question by saying he was "not in the House of Parliament."
The former Swindon manager, who is Martin O'Neill's successor at the Stadium of Light, stated in a 2005 interview with an Italian news agency that he was "a fascist, but not a racist."
His appointment led to the resignation of former foreign secretary and the club's vice-chairman David Miliband, who said in a statement, "in the light of the new manager's past political statements, I think it right to step down."
ITV News correspondent Martin Geissler reports:
In a news conference this morning - which was cut short after repeated questions on the Italian's political beliefs - Di Canio said he would only talk about football.
The Durham Miners' Association has asked Sunderland to return a symbolic banner which is kept at the Stadium of Light if Di Canio remains in his post and described his appointment as a "betrayal and a disgrace".
Asked if he would meet the association, Di Canio, who has been pictured making a fascist salute to Lazio fans in the past, said:
The Italian also insisted that the controversy surrounding his appointment would not affect his squad, who are in a relegation battle.
Anti-racism group Kick It Out expressed concern about far-right groups in football and called on Di Canio to state a commitment to equality.
Meanwhile, The Nelson Mandela Centre of Memory, which has a partnership with Sunderland, released a statement reaffirming their commitment to the club.
Shirt sponsor Invest In Africa told ITV News they were "reviewing" their partnership with the club but denied that the review was down to Di Canio's controversial appointment.