More inward and lasting than
抱歉 (bàoqiàn, 'sorry; apologetic').
抱歉 is what you say when you're late;
歉疚 is what you feel for years about something you did to a loved one. Common collocations:
深感歉疚 ('feel deeply remorseful'),
心怀歉疚 ('harbor guilt'),
满怀歉疚 ('full of remorse').