I believe contemporary Middle or New Kingdom Egypt had a population of 2-3 million at the time?

As a rule of thumb, urban population in those days usually represent about 5-10% of a local regions total population, so you can calculate a rough estimate of the total pop by multiplying combined population of city centers by a factor of 10 to 20.

More accurate estimates will require at minimal assessing the food production capacity of the area in question, ideally paired with records from the locale (which the city-states of Mesopotamia made plenty of in the form of cuneiform clay tablets recording taxes and temple contributions). I'll see if I can dig up something..