Know What You Are Returning To
There may be two issues: the original disagreement and what happened during the argument. A conversation about a practical problem will not necessarily address a hurtful remark. We can separate those concerns so one does not keep overtaking the other.
Be Specific About Your Part
A useful acknowledgment names an action rather than offering a general statement that everything was unfortunate. We can explore what you are able to take responsibility for without accepting an account you do not believe. Listening to the impact of an action is also different from agreeing with every interpretation.
Discuss the Next Conversation
Repair is not only about looking back. We may identify what to do when the same topic returns: how to raise it, when to pause or what each person needs to understand. An agreement is something to examine in practice, not proof that future conflict will disappear.