Gretchen Rubin is a blogger on happiness and provided these fight phrases, which I have found through personal use, have dissolved situations. They are usually with spouses, but others can apply:
"here are twenty-three phrases that help turn down the heat of anger:
Please try to understand my point of view.
Wait, can I take that back?
You don't have to solve this--it helps me just to talk to you.
This is important to me. Please listen.
I see you're in a tough position.
I can see my part in this.
I hadn't thought of it that way before.
I could be wrong.
Let's agree to disagree on that.
This isn't just your problem, it's our problem.
I'm feeling unappreciated. [Always, my craving for gold stars!]
We're getting off the subject.
You've convinced me.
Let's take a break for a few minutes. [If you can remember to do this, it's extremely effective - especially if you're having a big fight. After a break, it's almost impossible to go back to yelling.]
Please keep talking to me.
I realize it's not your fault.
That came out all wrong.
I see how I contributed to the problem.
What are we really fighting about?
How can I make things better?
I love you."