Here’s what McEvedy and Jones’ Atlas of World Population History says:

In the final millennium BC there was an even more dramatic boom and bust. The political expression of the boom was the Assyrian Empire, the creation of the city state of Assur at the northernmost point of the irrigating area. The number of Assyrians must have been tiny—a few tens of thousands at most—but as in the case of Rome a few were enough to conquer the world as they knew it. By the seventh century BC Assyrian governors were installed throughout the Near East from Egypt to Iran: a steady stream of captives and adventurers flowed into the new capital of Ninevah, bringing the total population of Iraq to an all-time high of 2m.

(McEvedy & Jones is forty years old now, but afaik it’s the only comprehensive attempt to reconstruct global demographic history on a regional level.)