As I was trying to reason in another thread, when it comes to Old Testament prophecies, there are both physical fulfillments of them as well as spiritual fulfillments of them in Christ. In each case we must consider seriously both the literary and historical contexts.
Regarding the question proposed in the OP, we must consider the fact that the Psalms were written during the time of king David, hundreds of years before both the Assyrian and Babylonian captivities of national Israel and their return and restoration afterwards.
In this particular Psalm the Psalmist is lamenting that the enemies of national Israel and of God's people are threatening to completely wipe them out. During this time it was not God's plan for national Israel to be completely judged by Him as was the case in AD 70.
One such prophecy I think is found in Psalm 83. When one reads this Psalm it reads pretty much like today's headlines. I cannot help but think that national Israel will play a prominent part in the return of Christ.The Psalm for an example mentions the Edomites. These are descendants of the Persians. Today Itan is considered old Persia. The Supreme Leader of Iran, the Ayatollah Khomeini, has made threatening remarks regarding Israel. To summarize these remarks would be that Iran will wipe Israel off the face of the map. Seems very similar to the Psalm on saying come let us wipe them out as a nation. I cannot help but wonder if this is being fulfilled today toward the nation of Israel.
Psalm 83 also mentions the Ishmaelites. These are descendants of the modern Arabs. Can anybody in the forum deny that the Arabs in the Middle East would love to see Israel wiped off the face of the map. Again I cannot help but think that this is being fulfilled today.
I don’t see any need for us to conclude that this refers to any of today’s Middle-Eastern nations. All these nations mentioned in this Psalm existed during the time of the penning of it. I think it’s a stretch to try to make this out to be more than a lamenting of the threats by these nations during the time the Psalmist penned these words.
That being said, spiritually we can apply it to today’s threats by the Enemy to wipe out the Church, the remnant people of God, the seed of Abraham (Gal. 3:29), the Israel of God (Gal. 6:16). God has always had and will always have a Church, a people for the praises of His name.