The fasting process is very much equal to resting and so when you do fasting you should not exercise.
But now it also depends why you are fasting.
If you are fasting to give your body time to rebuild itself, then you should better rest because the goal of fasting is not to not eat but rather to give your body a good rest and time to heal.
If you happen to be fasting only for a few hours because of a medical intervention of just because you haven't eaten yet that day or not hungry then it really depends how your body feels.
If you're not feeling good because you exercise while having been fasting for a few hours then by all means you should probably avoid it.
That been said it's better to exercise on an empty stomach so in a way you're kind of always fasting as long as you're not eating
Bottom line is if I were you I would not exercise in any case just before a medical procedure, especially while fasting.
Running on an empty stomach is certainly ok but if you feel any symptoms from doing that you might want to try eating something light half an hour to an hour before running.