Di Canio, winner of a Fair Play award while with West Ham, hit back and said: "I wouldn't want to have dinner with Totti. If I spoke to him about the Middle East he'd probably think I was talking about an area of the football pitch.
"I know I'm not intelligent but he's at another level completely."
Di Canio then accused Totti of being arrogant after he told Roma officials to buy more star players or he would leave.
Totti hit back by saying Di Canio had no real devotion to Lazio. He also said that if he wanted to make jokes he should have told him and he would have put them in his book which was published last year.
The Rome-Lazio derby is always a tense match and police had asked for the evening kick-off to be rescheduled to the afternoon, but Serie A officials refused.
In last year's abandoned match, 153 officers were hurt while 14 fans needed treatment after a false rumour swept the crowd that a child had been knocked down and killed by a police car.
Both sides started the season poorly, although Roma have now bounced back and are climbing up the table while Lazio are near the bottom.
Roma coach Luigi Del Neri said: "Francesco is mature enough to know he shouldn't let these sort of things get to him. We will see on the pitch his response. Personally, I think Di Canio said these things to motivate Lazio, not to provoke us.
"It was all said in fun and we are approaching the match in a good frame of mind."
Meanwhile, representatives from both sets of supporters promised they would not let the row get to them.
Rodolfo Bada, a senior organiser of the Lazio fans, said: "We are not interested in the squabble between Di Canio and Totti. We are not going to let their row get to us. However, it has been amusing to watch. We just want to win."
Roma's representative, Alberto Mandolesi, added: "I'm sure there will be some good-natured banter between the fans about the Di Canio-Totti row.
"But at the end of the day the match is Roma against Lazio not Di Canio against Totti, and that is what counts."
Both added that collections would be made during the match for victims of the tsunami disaster in South-East Asia.
