Sometimes in life you have to not be apologetic but still have to refuse some requests without being blunt and inappropriate to the person requesting it . In those events one must choose his words very carefully ,you have to be kind and able to connect with that person ,also make the person feel that you completely understands the situation of the person . Many times in some cultures or parts of the world saying sorry directly or at the very beginning considered to be very rude. In these situations you to be work your way around to first feel the emotions the other person feeling and make them feel in what spot the other person is and then after this buffer you say sorry or it may no longer be needed.

Saying sorry in the very first sentence is like rejecting the person rudely on the face it doesn't help in maintaining the future relations with the requester in the same way as they were before .

How to work your way around -just tell or explain your situation that how you really want to attend the particular function and how you because of some extremely important work  cant attend it and how much you regret it .These all things helps saying no easier with out hurting the feelings of the other person and also the relations with them.