I am not a nurse yet but I encounter this a lot. If someone asks me to pray for them (not at that moment), I say things that are reassuring and true, such as "you will be in my thoughts" and I make it clear in conversation that I do care about the outcome of the situation, want the best for them, etc.
Being asked to participate or lead a prayer is a lot stickier.... Maybe you could say something like, "Can I sit with you while you pray?". If it is an extremely uncomfortable situation (like the 5th prayer session that hour), try something polite but firm such as "I am going to let you and your family have some privacy" and step out if you can.
If the patient is simply scared and looking for comfort, I can't imagine they would be insistent that you
do the talking. They just don't want to be alone at that moment. (and thus began religion, but I digress....