Horse-drawn war chariots were used in 2000 BCE, but they came into prominence and were extensively used in battles between 1700 BCE and 700 BCE.
The first chariots are believed to have originated in the Eurasian steppes in 2000 BCE. In the early 2000 BCE, chariots were used in Mesopotamia to transport trade goods and agricultural products. Mesopotamians had later created wagons to carry a ruler and his soldiers to the battlefield. These battlewagons with four solid wheels were heavy and decreased the momentum.
The introduction of the horse and the spoked wheel in about 2000 BC was the step in developing the chariot into a military arm that revolutionized warfare in the ancient world by providing armies with unprecedented mobility. Drawn by horses, with lighter carts and spoked wheels, chariots gained their status as an elite weapon and transport. The first known use of horse-drawn chariots in the war was in 2000 BCE during Kadesh's battle by the Hittites of Anatolia, the Hyksos in Egypt, the Aryans in northern India, and the Mycenaeans in Greece. There is evidence showing the use of war chariots in India in 1500 BCE and the Chinese provinces during the 1200 BCE.
However, the two-wheeled war chariots carrying an archer and a driver, combined with the composite bow with fully revamped military tactics, came to prominence by around 1700 BC. Full-scale battle chariots were first seen in 1457 BCE in a war between the Egyptians and some west Asian forces. From that point on, chariots were used in many wars across Europe and Asia.
Recent archeological excavations have found remains of horse-driven chariots in the ancient Harappa region dating back to 3500 BCE. But since this theory has been disputed and not fully validated, 2000 BCE remains the first known period where horse-driven chariots were used. Chariots were used in India, China, and other Asian countries, even in 200 BCE through a few centuries into the ADs.
Thus, we can say that transport and war chariots driven by horses were in use as early as 2000 BCE, but their extensive application in battle was seen between 1700 BCE and 700 BCE.