The correct answer is option B: Mongols.

Explanation:
The Mongols ruled over very sophisticated urban societies during their empire's peak in the 13th and 14th centuries. Under the leadership of Genghis Khan and his successors, the Mongol Empire stretched from China to Eastern Europe, encompassing a vast amount of territory.

1. Mongol Empire:
- The Mongol Empire was one of the largest land empires in history, covering a significant portion of Eurasia.
- The Mongols were highly skilled warriors and conquerors who had a strong military organization and tactics that allowed them to expand rapidly.
- They established a centralized government, with Genghis Khan initially ruling as the Great Khan and later his descendants taking control.

2. Urban Societies:
- The Mongols ruled over various sophisticated urban societies within their empire.
- Cities such as Karakorum (the capital of the Mongol Empire), Samarkand, Bukhara, and Tabriz flourished under Mongol rule.
- These cities became important centers of trade, culture, and administration, attracting merchants, artisans, scholars, and religious leaders from different regions.

3. Cultural Exchange:
- The Mongols promoted cultural exchange and communication among the diverse peoples within their empire.
- They facilitated trade along the Silk Road, which connected Europe and Asia, leading to the exchange of goods, ideas, and technologies.
- The Mongols also had a policy of religious tolerance, allowing different faiths to coexist peacefully within their empire.

4. Administration and Governance:
- The Mongols implemented a highly efficient administrative system to govern their vast empire.
- They appointed capable administrators and officials to manage different regions and ensure the smooth functioning of their empire.
- The Mongols also established a postal system, known as the Yam, which facilitated communication and the efficient movement of goods and information.

5. Legacy:
- The Mongol Empire had a lasting impact on the regions it ruled over.
- It facilitated the spread of knowledge, technologies, and cultural practices across different regions.
- The Mongols' rule also influenced the development of various urban centers, trade networks, and administrative systems in subsequent centuries.

In conclusion, the Mongols ruled over very sophisticated urban societies during their empire's peak. Their military prowess, administrative skills, promotion of cultural exchange, and efficient governance contributed to the development and prosperity of the cities and regions under their control.