'To fast' means to stop eating all or certain foods or meals and is most often done as a religious observance. In this case the person obviously intends eating nothing until he gets what he is asking for even if he dies as a result. We also use the expression 'to go on a hunger strike' or you can say 'to starve yourself to death'.

'fast' here is a verb in the sense of abstain from eating, not the adjecitve that means 'quick'. So he intended not to eat until he dies, unless Singh agrees .... I am not sure if the sense here is literal and he is intending to literally abstain from food?!