Icardi, who only recently signed a new long-term contract at San Siro, is currently under fire from the group, who have taken exception to comments made by the forward in his autobiography.
Curve Nord, who have branded Icardi "a vile piece of s***", have issued a statement demanding that Inter take the captain's armband away from Icardi, amid claims that the Argentine threatened to bring over criminals from Argentina to kill the club's ultra group.
Ahead of Sunday's Serie A clash with Cagliari, which Inter lost 2-1, Icardi penned a letter in a bid to defuse the situation, but he was roundly booed during the league match at San Siro.
"Dear Curva Nord, I am surprised and disappointed," Icardi wrote on Instagram. "I am surprised because I simply referred to the fact I lost my temper in the heat of the moment, combined with the adrenaline of the match and the bad moment the team was going through.
"I simply wanted to sum up the atmosphere of that incident. It's true that in the book I spat out some exaggerated phrases (and the verb spat gives a good idea of how inopportune my reaction was).
"As for the issue of getting assassins from Argentina, as people continued to tell me that I would've found some hooligans under my house (note: not the Curva Nord members, but hooligans), I said that phrase. In the biography I also wrote that 'I used threatening words towards the fans and I shouldn't have done that.'"
"I am disappointed. Disappointed with the chaos that has been brought up. I simply gave my recollection of an incident. If I had the slightest brain in my skull, I certainly wouldn't have risked offending the curva. I didn't want to offend or disrespect anyone.
"The captain's armband represents the realisation of my childhood dreams, the joy that I gave first of all to my family and then to myself. You are the ones who I look out for every Sunday after scoring a goal, it is your embrace I seek first, because I love Inter."
"Imminently I will step on to the field, so I can't go on any more. I hope you understood how important you are for me and how much respect and love I have for you, even if you decide to jeer me. I ask you just one thing as captain - stay close to Inter, as you always have done, because my teammates and I need you. With affection, Mauro."
The spat started when Icardi criticised a member of Inter's ultra group over an incident when he tried to give a young fan his shirt after a game.