Final answer:
Around 650 BC, the Neo-Assyrian Empire controlled the territory in question, known for its military and cultural prominence.
Step-by-step explanation:
Around 650 BC, the area within the red line you're inquiring about was most likely under the control of the Neo-Assyrian Empire. The Neo-Assyrian Empire, originating in Mesopotamia, was at the peak of its power during this period under the rule of kings such as Ashurbanipal. This empire was known for its advanced military organization, notable cultural achievements, and powerful administrative structure.
Not far from this time, the rise of other ancient civilizations, such as the Achaemenid Empire under Cyrus the Great, would come into prominence. By 539 BCE, Cyrus the Great captured Babylon and incorporated Mesopotamia into what would come to be the Persian Empire. The Assyrians, though formidable, eventually faced internal strife and external challenges, including from the Medes, Babylonia, and later the Persians.