You may not have much of an obligation towards him but if you consider him a friend and still are friends, there is nothing wrong in giving him 5 mins of your time so he can get his closure (if that's what he intends on doing)!
I do know there are certain girls out there who love *constant attention* from guys they have rejected (not specifically talking about you), but yes many girls do indulge in stringing guys along in the name of friendship. If you don't care enough, like other suggested break off the friendship and be done with!
But if you do care, then yes as a friend, you should care enough about his feelings if he simply wants a closure. And he should too if you explain it in plain words it is making you *uncomfortable* - I can't really take any side here cuz clearly the dynamics you share only you two are aware and only you two can decide how to wrap it up.
Won't provide any unilateral support here unless we can hear both sides equally. But that's just me!