Don't make a big thing about it, but try lots of positive statements about other things - things she's good at, good behaviour - so you boost her confidence in other ways.
Downplay it when she talks about being fat. If she says she's fat, just say breezily "Of course you're not fat", and change the subject. Don't be drawn into a conversation with her about it because that will reinforce in her mind that she is right. Turn it into a non-issue.
I would also be careful about saying that "she's not fat and you love her as she is". She doesn't understand that you mean you love her unconditionally; bundling the two things together may lead her to associate being loved with being either thin or fat.
I'd also have a quiet word with the nursery staff (outside of her earshot) and ask them to keep an ear out for other children saying things.
And Custy is right - if she refuses to eat, leave her. Don't make any comment, don't make any fuss - just take the plate away. When she's hungry she will eat.