Di Canio, 44, replaced Martin O'Neill at the relegation-threatened Premier League team on Sunday, a move that sparked the resignation of a British former government minister from the club's board.
David Miliband, a departing Member of Parliament and a former Foreign Secretary, stepped down because of remarks the ex-Swindon Town boss made to Italian news agency ANSA in 2005 when he said: "I am a fascist, not a racist".
"I don't have to answer any more this question, there was a very good statement from the club, [with] very, very clear words that came out from me," the Italian said on Tuesday in an effort to steer talk away from politics and back to football.
"I don't want to talk any more about politics for one reason because I'm not in the House of Parliament, I'm not a political person, I will talk about only football."
Di Canio had sought to dampen the fires on Monday by releasing a statement that suggested he had been quoted out of context.
"I expressed an opinion in an interview many years ago. Some pieces were taken for media convenience," he said.
Di Canio's appointment led the Durham Miners Association (DMA), a powerful workers' organisation in the north-east of England, to ask for the return of a banner that is on permanent display at the club's Stadium of Light.
"The appointment of Di Canio is a disgrace and a betrayal of all who fought and died in the fight against fascism," the DMA's general secretary Dave Hopper said.
"Everyone must speak out and oppose this outrage and call on [club chairman] Ellis Short and the Sunderland board to reverse their decision."
Asked if he had a message for the DMA, Di Canio said: "I have said many, many words in the past and people have picked the words they wanted. I can't keep going on about my life and my family. The people who are talking in this way, they don't understand Paolo Di Canio."
The Italian was given the job after a 1-0 defeat to Manchester United on Saturday prompted the surprise sacking of O'Neill.
Sunderland are 16th in the 20-team table and without a win in eight games.
Asked whether he thought he could steer Sunderland away from relegation danger, Di Canio said he would bet everything he had on them not finishing in the bottom three.
"When I got the call from Ellis Short, I felt fire in my belly. I would have swum to Sunderland to take the job," he added.
"The press like to call me the mad Italian but I would confidently bet everything I have on Sunderland remaining in the top flight."
Di Canio had a colourful playing career with clubs including Juventus, AC Milan, Lazio, West Ham United and Celtic, but has never managed in the top flight and joins Sunderland six weeks after quitting third-tier Swindon Town.
Never far from the headlines, he is remembered for pushing over a referee while playing for Sheffield Wednesday in England and drew outrage in 2005 when he celebrated his Lazio side's derby win over AS Roma with a fascist-style salute.
"With my energy I'm sure we can get something f
