There are many ways of saying "sorry" in Turkish...
1- Özür dilerim.
This phrase is generally used in order to show that you are deeply sorry due to what you did. It is better not to use this phrase unless you did something really bad. Here some examples.
Özür dilerim. Kalbini kırdım. (I'm truly sorry. I broke your heart.)
2-Pardon.
It is a casual way of saying sorry... It does not have a strong meaning.
Pardon bakar mısın? (excuse me?) (to grab attention)
Pardon oturabilir miyim? (Sorry, Can I sit here?)