Are they all ok?
It's I who must apologize.
It's me who must apologize.

It's I who should thank you.
It's me who should thank you.

Question

Are they all ok?
It's I who must apologize.
It's me who must apologize.

It's I who should thank you.
It's me who should thank you.

Answer

It's I who must apologize. = Shakespearean, correct but outdated.
It's me who must apologize. = The modern version.

Answer

It is I, who must apologize
It is I, who should thank you

is correct English, though this rule is broken so many times when people speak !

http://www.dailywritingtips.com/its-me-vs-it-is-i/