Remorse

Try these phrases, “I apologize” and “I am sorry.”  These two phrases belong in every apology. 

Any other phrases just won’t do.  For instance, “I want to apologize” may sound like an apology, but is no more about actually apologizing than “I want to lose weight” is about actually losing weight. 

What your co-worker offered is an intention to apologize, which is a good start but far from an apology itself.  It is always appropriate to express regret and a commitment not to repeat the offensive behavior.