"I want to categorically deny that I made any kind of racist insult towards any Sevilla player," the Spanish international and former Arsenal captain wrote on his Twitter account after local media reported the accusation.
"I will not tolerate anyone accusing me of things that I'm not," added the 24-year-old.
"If they are frustrated by a decision that has gone against them on the football pitch then there are others ways to deal with it.
"To cry racism is cowardly and an easy option to excuse your own poor behaviour. My conscience is completely clear. I've done nothing wrong."
Kanoute said he had been "provoked and insulted" during a mass brawl which erupted after Barca were awarded a penalty in second-half stoppage time. He did not mention Fabregas by name or use the word racist.
Before the penalty kick was taken, an angry Kanoute kicked the ball away from the spot and appeared to grab Fabregas around the throat before being sent off. Lionel Messi's effort was then saved by goalkeeper Javi Varas.
Kanoute wrote on his Twitter account that he regretted the incident - which came at the end of UEFA's Football Against Racism in Europe (FARE) week - saying it "was not a good example."
"Nonetheless there was provocation and insult, as you are already aware," the former Tottenham Hotspur player said.
"But don't think about it anymore. His behaviour, like mine, was bad. Issue closed. Let's get on with the football."
Fabregas and Kanoute later spoke by telephone and said they had said sorry.
"We both apologised and agreed the matter was settled," Fabregas tweeted.
Kanoute added on his Twitter feed: "The issue was explained and we are both adults and aware that we were at fault yesterday. The matter is closed."
Fabregas's Barca team-mate Daniel Alves defended the Spaniard at a news conference following a Barca training session on Sunday.
"There are moments when your pulse is racing and you don't say please when you are asking for things," the Brazilian defender said.
"But it's clear there was no racist insult, above all from Cesc, who is a fantastic lad and would never do that."
