There wasn't.

There was in Egypt, but the rest of the ancient Near East generally ascribed to corporate forms of political structuration. "Corporate" is a term adopted from Richard Balnton's "Dual Processual Theory" of state formation. Basically, there are two modes of political power manipulation he understands to be present in most societies. On the one hand, you have corporate political strategy, where the lion's share of socio-political power and control rests in the hands of groups rather than exclusionary agents. The ancient Near East was generally characterized by this form of political strategy, from as early as the Ubaid period. The persistence of groups like "elders" and "prophets" in cultures like ancient Israel and Aram attest to the salience of the political strategy. The other political strategy is "exclusionary." In this mode, power generally rested in the hands of singular individuals—exclusionary agents like pharaohs or kings. We can see remnants of such political structuration in the pyramids, the texts that describe Pharaohs as gods, etc. The archaeological reality of the Central Highlands in the southern Levant during the Late Bronze and early Iron Age, however, appears to attest to corporate political structuration. This is in part related to nascent Israel's prevailing egalitarian ethos (see Israel's Ethnogenesis by Faust).

Both Blanton and Avraham Faust (see also Dan Fleming [Democracy's Ancient Ancestors] and Brenden Benz Life Before the Kingdom of Israel) highlight how the ancient Near East generally eschewed exclusionary forms of power in favor of corporate. However, this changed over time That is to say, groups of secondary elites held the Lions share of the power. This was exhibited in the archaeological record in monumental architecture, among other things.

/u/Iphikrates — hope this is better.

I'm not as well-read as I'd like on the Persian empires or Egyptian kingdoms. However, I believe I can shed some light on the other half of your question, though more by questioning your premises, I'm afraid. Note that from here on out, I'm referring to the "Western Mediterranean" a bit unconventionally--traditionally, it's defined as everything west of the Adriatic, but for the sake of simplicity I'm pushing the line back roughly to the Aegean Sea or so.

It is true that during the classical period, a number of western Mediterranean realms were in some way democratic or republican--among others, the Roman republic, Carthaginian republic, Achean League, and (in an earlier period) Athenian democracy certainly fit the bill, and one of the more famous Greek city-states, Sparta, was ruled by a diarchy of kings, rather than a single ruler.

But these civilizations were not wholly republics by any stretch of the imagination. Greece was far from entirely democratic--though "traditional" Greece in the southwest continued to have a fairly strong democratic tradition, almost everywhere else Alexander the Great touched was a kingdom. Macedonia, for example, was decidedly hereditary; during a similar time frame, Epirus (in modern-day Albania) was also hereditary, and although though I'm not certain how absolute the monarch was, it was decidedly not a co-rulership akin to Sparta. Additionally, a number of other monarchies existed on the Hellenic periphery throughout the period, like the Pontic Kingdom on the north coast of Anatolia and the Bosporan Kingdom in and around Crimea. Depending on how influential one considers the common people versus the government, one could even argue that the post-Alexandrian Seleucid Empire and Egyptian Kingdom--both of which were fairly absolute, as far as I know--were more Greek than Persian or Egyptian.

Rome is a particularly interesting case here, because its famous republican leadership was intrinsically tied to its prior lack of republican leadership. Though the original records of early Roman leadership were destroyed in the first Sack of Rome, most Roman historians agreed that the Romans had originally been led by kings of Rome, and pointed to the tyranny of the seventh and final Roman king, Lucius Tarquinius Superbus, as the reason their kingdom became a republic.

The 'seven kings of Rome' are by modern historians generally considered to be legendary--that is, they were real in broad strokes, but were probably composite characters drawn from a number of different actual historical figures, whose lives were likely heavily mythologized into borderline fables or moral lessons. However, it's generally agreed that Rome was originally a kingdom, and the inhabitants of the Republic certainly believed that the kingship was ultimately responsible the existence of the Republic.

I also mentioned Carthage earlier. I'm not as familiar with the Carthaginian republic as much as the Roman one, but I do know that it purportedly had a similar experience to that of Rome. Allegedly, Carthage was founded as a monarchy by the legendary Queen Dido; though whether or not Dido was even real is up for debate, it is clear that Carthage was ruled by kings--entrusted with many responsibilities, authorities, and military duties and elected by the oligarchic Carthaginian senate--until they were replaced by the popularly-elected, more limited suffets following defeat in the 1st Sicilian War.

Overall, there was certainly a republican or democratic presence in many parts of the Western Mediterranean, particularly as classical antiquity progressed. However, it was far from all-encompassing, and in two of the most famous cases, more or less directly descended from the prior existence of monarchy; at the same time, much of the Greek world remained under the dominion of monarchs at least until Roman authority was imposed.