We all care about others’ feelings a lot, especially when we say NO. Especially in Korea, saying NO politely is very important, and that’s why we have so many indirect phrases to say it. Trust me, even as a native speaker, I’m not an expert of picking up the best “no” phrase… I will introduce three most common phrases today, the rest depends on your own creativity. 🙂
(1) 생각해볼게요 (I’ll think about it)
This phrase gives an impression that you’re taking the other person’s offer seriously instead of rejecting it right away. If you want to be even more polite, you could specify how much more time you need.
(2) 미안해. 사정이 생겨서 못할 것 같아. (I’m sorry. Something came up)
This is another common phrase to say NO. ‘사정’ sounds a little private and serious, so the other person might not dare to ask exactly what happened to you unless he/she is very close to you.
(3) 미안해. 급한 일이 생겨서 못할 것 같아. (I’m sorry. Something urgent came up)
This means basicaly the same with “미안해. 사정이 생겨서 못할 것 같아.” But since you used “일” in this phrase, the other might ask exactly what happened.
Please keep in mind that you cannot overuse those phrases, because it will eventually give others have a bad impression of you just throwing out excuses.