E-Hamzeluyi's made good suggestions up there. Here's some more:
1.
A: Hey You eat?
B: No, thanks I'm stuffed/I just ate/I've had plenty/I'm perfectly satisfied.
I like stuffed esp.:
(Funny because it's a pun. Stuffed can mean something else here, too. :-))
2.
You could use fill your stomach to mean سیرکردن as in
When he finally got to eat, he filled his belly until he could fill it no more.
It's OK to use 'satisfy your hunger' to mean شکم خود را سیر کردن as in
He satisfied his hunger with a sandwich and milk.
However, in everyday convesations people simply use 'eat' to mean that.
I'm starving and there's nothing here to eat (instead of saying 'nothing here to feed myself or satisfy my hunger)
I'm starving. What is there to eat? (instead of using feed or satisfy)