I think that the administration of justice brings peace to a civilized society. Without justice, or perceived justice, can we really have peace? Sometimes peace is disrupted because of unjust practices.
Without justice, there can be no peace. At least, that's what Archbishop Oscar Romero said once. Being that he was pursuing social justice in war torn El Salvador, right before his assassination, I would say he knew about the relationship between those two ideas.
Peace on its own can be achieved a number of ways, including through the use of force or the denial of civil liberties, so I would say justice is the faster route to peace.
There are times when justice is eliminated in pursuit of peace. Many dictators and tyrants have claimed to do their repressive deeds in the name of peace. It is a good way to sell the idea that it's ok to take away freedoms. Whenever we trade freedom for security, we lose an element of justice. As we get closer to dictatorial society, there will be no justice or peace.
Your question is very vague because you do not provide a frame of reference, however an interesting one. As civilizations became increasingly complex it was necessary to ensure the 'peace' within a society.This was achieved by establishing laws. Law can be defined as a rule of conduct or action enforced by an authority in any given society. As interactions between diverse civilizations of people developed, laws that preserved the peace were expanded to serve justice, which inturn would preserve the peace. In some ways it could be argued that 'peace' is what most people want, but whether fortunate or not, 'justice' enforced by law helps to 'keep the peace'.
That's a tough question. I would say that peace must come first. In order to have justice, man needs to establish laws by which all people agree to be bound. In a state of war, it is difficult to establish laws because usually a state of war means that the warring parties have yet to agree on principles and values that will guide the formation of laws. And without laws, there can be no justice.