When child says "I'm sorry" many times the child who has been "wronged" says, "It's Okay". I have heard this scenario numerous times while teaching and at home with my own children.
The problem is the first child hears "It's Okay" and in the back of their mind they think "If it's okay, then I can do that again."
I tell the child who has been wronged, that they should say "I accept your apology, but I don't like it when you do or say that. Please don't do or say that again."
In this way the aggressive child hears that the other child doesn't like what happened and should not do or say it again.
Many times the aggressive child will say that they don't like what the other child did at an earlier time. Hopefully, the children will realize how they each can understand how the other feels. Compassion for another person's feeling is a great lesson for everyone.
This is a good way to reflect on what you have done and then set out to apologize in a meaningful way.
An apology is very important.