While I have always taught that in British English ‘excuse me‘ is used before disturbing a person and ‘sorry‘ after you have disturbed them, Italian “apologies” are a little more complex.
Much will depend on the form of address, ie. if you’re using tu, Lei or voi (see previous post), and of course on the context therefore:
“Excuse me” for interrupting someone wil be be a form of the reflexive verb scusarsi, therefore:
“scusami” (informal), “mi scusi” (formal) or “scusate” (plural) – but these are also used for saying ‘sorry‘ ie. after disturbing, or as in brit English “Sorry?” if you haven’t heard what’s just been said.
Sorry can also be ‘mi dispiace‘ although only in the sense that you are generally sorry about something (apologising for mistakes, loss, death,….)
Don’t confuse “perdonami” or “mi perdoni” with “pardon me” as it means ‘forgive me‘.
The verb ‘to apologise’ is the reflexive ‘scusarsi‘ or ‘chiedere scusa’ (see chiedere in verb tables) so you may read the very formal “vorrei scusarmi per..” or “vorrei chiedere scusa per..” – I would like to apologise for..
“Massimo Tartaglia, ha inviato questa sera una lettera di scuse al premier, esprimendo il proprio dispiacere per il gesto.”