I agree with Victoria W. that you should make the whole experience as calming and comforting as possible (a child's potty seat would be ideal), and gently lead her with questions to find out what part of the experience is upsetting her. Have you ruled out the possibility of a UTI or exterior irritation of the vulva? She could feel a sting when she pees.
Something I've tried with success when children are afraid of something is to act it out with puppets or stuffed toys. Include and validate the fear or anxiety, move past it playfully, end with success. This is a hit with my grandson, who was terrified of having scrapes washed, and for awhile suffering with difficult poops.
Try this the first few times when your daughter doesn't need to use the potty, so her anxiety level will be as low as possible. Have one toy be the anxious "pee-maker," and another ask questions. You could even have several anxious players take turns. The script could go something like this, with characters A and B:
A: Oh, I have to pee, I have to pee!
B: OK, let's go. I'll help you. (Go to the bathroom.)
A: I don't want to get on that big potty…
B: Oh, does the potty scare you?
A: A little bit.
B: Are you afraid of falling? (Try out various possible fears if this one doesn"t register.)
A: Yes, a little bit…
B: I understand. That hole is big, isn't it? Do you want to pee in your diaper instead?
A: No, I want my big girl panties! Can I have my big girl panties?
B: You are getting to be a big girl. I'll help you use the potty if you want. I'll hold you very carefully, and you can keep your feet on the stool.
A: Well…okay, I'll try. (sits) Oh, oh, I want down. Maybe next time.
B: That's okay, maybe next time. Everybody's kind of afraid at first. It feels funny, doesnt' it?
A: Yes, I don't like the way it feels.
B: So, it feels like (list as many ideas as you can, with A saying YES! each time). Ah, I get it. I remember feeling that way. And you know what? As soon as I did pee, I felt SO GOOD! And SO HAPPY! And after awhile, I felt so good while I was peeing! Watch how I do it! (Demonstrate with puppet, with B getting into a little "song" like:
B: "I feel up high, yes… that hole feels big, yes… Mommy is holding me, yes… so I feel a little bit safe, yes… I'm worried about letting go, yes… oh, I'm letting the pee go, yes… OH, I'm doing it!, yes… I'm PEEING!!!, yes… Yay, I DID it! YES!
A: Okay, can I try now? (Repeat B's little song).
B: You did it!!! You know what? That was a very brave thing for you to try, and next time will be even easier. Pretty soon, you'll find out you're not worried about peeing any more, and you'll be using the potty just like a big girl. Congratulations! (Avoid saying YOU ARE very brave, because that could be a hitch if your daughter doesn't feel brave yet.)