Yes, is perfectly natural. It's politer than but less polite than . Hotel clerks may stick to , and you should use in a serious formal apology, too, but there are cases where is enough.
**EDIT:** For example, if you're saying "I'm sorry" to your close boss in the same section, can be an overkill, and I usually say or . Of course this largely depends on your workplace, so if everyone around you is saying even in this situation, you may want to do the same.