The moment Michael was invited by Tessio to a meeting with Barzini it was kill or be killed and he had to act first. Without Tessio on his side Michael would lose half his manpower and he would've never won another war with the other families. However, as long as Vito was alive I don't think Barzini would've made a move on Michael, nor do I think Tessio would've betrayed them.

I think Barzini chipping away territories from the Corleones could be considered breaking the peace from their point of view, but technically he would only break the peace if he would've gone over to violence.