A refusal can sound abrupt when the listener was expecting to negotiate past it.

A plain no is often heard as rude for a reason that has little to do with how it was said. The listener expected the first refusal to be an opening position, something to be worn down with a little more explanation. When it turns out to be the actual answer, the surprise gets experienced as harshness. Softening your language will not fix that, and usually just invites another round.

So let a no be short, warm and repeated in the same words if it needs repeating. You can be sorry about the disappointment without treating the decision as still open.