Hart is under pressure after a poor start to the season.
Pellegrini said: "For the moment Joe will continue being our goalkeeper but I spoke with him and he knows he must be quickly in his top form again.
"I am sure he is a top goalkeeper and will do it again. I said from the beginning my teams never play with names, they play with performances.
"Joe knows perfectly he needs good performances in the next games. At the moment he has all the trust."
When asked if Hart could be dropped, Pellegrini added: "I think it is not the moment.
"That doesn't mean we don't have another goalkeeper. We have Costel Pantilimon. But we know Joe has had a difficult moment and those players need trust in those moments."
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