It's common to use 'Excuse me, ...' before interrupting someone to ask for something in English. Another, more formal form is 'I beg your pardon ...'
Person 1: Excuse me, do you know what time it is?
Person 2: Yes, it's two o'clock.
Person 1: I beg your pardon. Would you minding helping me a moment?
Person 2: Certainly. What can I do to help?
In these cases, people are asking for help but begin the conversation by apologizing. If you would like to apologize for something that you have done wrong, or misunderstood, the following phrases are appropriate:
I'm very sorry for / that ...
I apologize if I ...
I apologize for (+ ing form of verb)
Example Dialogues
Person 1: I'm very sorry for stepping on your foot!
Person 2: Don't worry about it. It's very crowded on this train.
Person 1: I apologize for my mistakes on this quiz.
Person 2: That's why you take quizzes - to learn!
