If by “just war” one means “good war”, I don’t think any Orthodox could support this.
However, if by “just war” one means “justifiable” or “necessary” war, then I think the Orthodox would have to accept this. I know this is the sense St.Augustine had when he addressed this topic.
As for the current campaign in the Middle East, for now I’ll simply say this for now…
a) It’s publically stated reasons have changed many times (hence it has no solid mandate)
b) I doubt it will end up doing more good than harm (either for the people in Iraq, or in the long run, for the people of America or other westerners).
c) Two of it’s key justifications (the presence of WMD in Iraq and that Iraq would have a realistic way of deploying them either against the United States or it’s allies) have shown themselves to be utterly false, and they were known to be false within the intelligence community prior to the invasion.
d) Further, it was heavily implied (as a means of selling the war to an understandably frightened American public) that Baathist Iraq had given significant support to the global Jihdadists, or that it served as a centre of operations for them. This is very very mistaken, and preys upon a popular ignorance by those not well read on the realities of the Middle East about the relationship between Wahhabi Jihdadists and the various governments of the Middle East (including Iraq.) While it is undoubtedly true that Saddam Hussein was a brutal dictator, “Baathism” (the ideology of his party) is a fundamentally secularist ideology, and the Jihadists have a deep resentment of such forms of government existing within what they regard as “historicall Islamic lands.” And while nothing excuses the brutality of Saddam’s regime, a large part of it was influenced by the fact that he ruled over a mixed population who would otherwise be killing each other either over conflicting tribal affiliations or such Islamically fundamentalist motivated pretensions of “institution Sharia”. This is intererestingly (and depressingly) precisely why Christians were safer under Saddam’s government than they now are (or will ever likely be) in Iraq (which is now in fact incorporating aspects of Sharia law into it’s official constitution and legal system).