The Bosnia international came close to leaving the Etihad Stadium after falling out with former boss Roberto Mancini but will be given a chance to prove himself by the new trainer
The Bosnia international dropped down the pecking order under former boss Roberto Mancini, but started the club’s resounding 4-0 victory over Newcastle on Monday night.
Dzeko linked well with Sergio Aguero and David Silva but Pellegrini insists the striker must score more goals if he is to nail down a regular starting berth.
Speaking to reporters, Pellegrini said: "Dzeko played well against Newcastle, but not very, very well because for all the things he did he must score. Then he will have played very well indeed. He had bad luck.
"Of course, I have no doubt he will score goals. He has scored goals throughout his whole career.
"I spoke with him before I arrived here and told him that if he will stay here this year, he must demonstrate the player that Manchester City bought two years ago.”
Dzeko’s future at the club looked in doubt after the conclusion to last season and speculation suggested he would be one of the first to depart the Etihad Stadium. Yet Pellegrini has restored the striker’s confidence.
The Chilean added: "Dzeko and a lot of players interest a lot of clubs. It’s very important for him to know that all of us trust him, not only me but also the other players, the club, everybody.
"I don’t expect a certain number of goals. The first thing is that the team wins. If the team wins, who scores is not the most important thing.
"Normally the striker will always be scoring, but in my team, normally all the players score goals. That’s very important.
"I don’t want to talk about last season. It’s not my duty. I know what I must do. My duty is to talk with all the players, not just one or two.
"They must know what I want of them and they must know that they are here in this squad because I trust them."
Dzeko, who arrived at the Etihad from Wolfsburg in 2011, has scored 30 goals in 77 Premier League appearances for City.