Anti-fascism campaigners have called for Paolo Di Canio to publicly retract comments about his political views.
Unite Against Fascism's joint national secretary, Weyman Bennett, said his appointment was "an insult" to the people of Sunderland:
Some Sunderland fans have said they support Paolo Di Canio's appointment, but cautioned that he must keep his political views to himself.
One season ticket holder, Stan Simpson, said some fans would be "wary" about the Italian's appointment but that he respected David Miliband for sticking to his principles.
"I understand Mr Miliband's decision but there is no way we, as fans, would entertain any fascism in our club. As long as he doesn't express any political opinions I can cope with it."
Janet Rowan, another fan, said she thought Di Canio was "very passionate" about the game but said extremist politics "isn't something we want in football".
She added: "I respect David Miliband's views but as fans we have got to support Di Canio."
Di Canio has admitted to having fascist leanings, telling Italian news agency ANSA in 2005: "I am a fascist, not a racist."
Paolo Di Canio has been appointed Sunderland head coach on a two-and-a-half-year deal, the club have announced.
David Miliband has resigned from his role as vice-chairman and non-executive director of Sunderland due to new manager Di Canio's "past political statements", the former MP said.
Sunderland Football Club have thanked their former manager Martin O'Neill for all his hard work.
It said in a statement, "The club would like to place on record its thanks to Martin and wishes him well for the future. An announcement will be made in the coming days regarding a successor".
Sunderland has announced it will "part company" with manager Martin O'Neill.