Pellegrini last week responded for the first time to Mourinho's regular jibes, and the Portuguese has since fired back yet again.
Mourinho's latest salvos concerned the decision by the Football Association not to take action against City midfielder Toure over an off-the-ball incident at Norwich last weekend, and calculations over the London club's transfer spending.
These came after Pellegrini responded to Mourinho's claim that Chelsea were the "little horse" of the three teams in the title race by saying they were "little, but rich".
Pellegrini had also suggested Mourinho was continually telling lies about City - there had been previous remarks about Financial Fair Play and luck with refereeing decisions - in the hope that some became established as the truth.
Pellegrini had previously refused to get involved in such tit for tat and the experienced Chilean, who clashed with Mourinho during their time in Spain, wants to revert to that position.
The 60-year-old said: "I answered just once to Mourinho because if you remain in silence always, (people) may agree with those things.
"He started talking about referees and Financial Fair Play, I don't think it is the way (to go about things).
"But just once. I will not continue every week talking about things that for me are not important."
Mourinho's frequent barbs have been depicted as mind games in a close Barclays Premier League title race but Pellegrini insists they will not work.
He said: "No, I don't think those are mind games. I don't think any managers can be affected by those kind of things."
An FA disciplinary panel opted not to take retrospective action against Toure after the Ivorian appeared to kick out at Norwich striker Ricky van Wolfswinkel.
The incident in Saturday's goalless draw at Carrow Road was missed by referee Jon Moss but caught on television and Mourinho suggested the Ivorian should face a violent conduct charge.
But Pellegrini, speaking at a press conference, said: "I repeat, I don't respond to things Mourinho says every week because he will continue every week to try talking about things that are not from football."
As for the incident itself, City might be relived that there is now no prospect of Toure facing a ban at a time when key players Sergio Aguero, Fernandinho and Samir Nasri are injured.
Pellegrini said: "I suppose the FA acts the way they think is better for all the teams. I trust in the FA and I trust in referees."
Mourinho claimed not charging Toure could effectively give players licence to "do whatever".
Arsenal manager Arsene Wenger did not support that theory when invited to weigh into the debate.
He said: "It is a decision we have to accept. This decision is questioned, and people who make these decisions can answer these questions. I do not know why they made the decision.
"One positive thing is that this committee exists and that the players know that they can be punished even after the game, so that is very positive.
"After that, the decision is made by human beings and then you have to accept we will not always agree on the way the decisions are made.
But it is a good thing that this committee and the whole (disciplinary) process exists."
Van Wolfswinkel himself has no issue with the FA's verdict and wrote on Twitter: "Good to see Toure not getting suspended. Players like him belong on the pitch! What happens at Carrow Road stays at Carrow Road.
"Things happen on the pitch. But we all enjoy watching him play. So get on with it and enjoy the football. That's what it's all about."