I'm sorry; excuse me; my apologies
A polite, somewhat formal apology or expression of regret, often used when leaving a room, ending a call, or after a minor mistake. More formal than すみません.
I'm sorry for leaving before you.
Before hanging up, I said, 'I'm sorry (for the intrusion).'
申し訳ございません is a more deeply humble and formal apology than 失礼しました, used for serious mistakes or in customer service.
失礼します is the non-past form used when entering a room or starting to leave, while 失礼しました is the past form used after the action is finished, such as when hanging up a call.
Polite past form of 失礼する (to be rude, to excuse oneself). The phrase literally means 'I have been rude' and is used as a set apology.