"He must apologise. If he doesn't, he won't play," Guardiola told reporters.
The 33-year-old player's agent Dimitri Seluk, who had said Toure felt "humiliated" after being left out of City's Champions League squad, hit back in similarly uncompromising fashion.
"What do I need to apologise for?," he asked Sky Sports television. "Guardiola wins a few games and thinks he is a king. I live in Europe so I can say whatever I like and Guardiola can't stop me.
"I will apologise to Guardiola if he will apologise to (former City manager) Manuel Pellegrini for what he did to him."
Toure, four-times African Footballer of the Year, has been a mainstay of City's midfield since joining from Guardiola's Barcelona in 2010.
He has only played once this season, in the second leg of a Champions League playoff tie against Steaua Bucharest when City had a 5-0 lead from the first game.
"It was difficult to leave him out of the Champions League squad but (the) day after, his (agent) went to the media. (Toure) has not had the courage to call me. From that moment he was out," Guardiola said.
The pair also clashed at Barcelona, with the player later telling a Spanish radio station that he felt forced out.
"He pretty much ignored me until City's offer came in. That's why I eventually opted to leave. I didn't speak to Guardiola for a year," Toure said in 2011.
"I did not want to go and wanted to end my career at Barcelona. However, he had no faith in me."
Guardiola said then that he had tried to convince the Ivorian to stay.
Toure, who had been tipped to leave after Guardiola joined from Bayern Munich in the close season, announced earlier on Tuesday his retirement from international football.
"Writing this note was probably 'the most difficult match of my life'," he said, adding that the decision was not to do with his age, intensity of training or number of games.
"Football is everything to me. It gave me so many things in my career that now I don't feel able to set new goals, as a player with the Elephants," he said.
Toure scored 19 goals in more than 100 appearances for Ivory Coast and captained his country to their first African Nations Cup win for 23 years in 2015.
Manchester City, who have a 100 percent record in the league after five games, play Swansea City in the third round of the League Cup on Wednesday.
(Additional reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
