During 2700 BC - 2300 BC, the Mesopotamians saw the first appearance of a Sumerian Abacus. Sumerian abacus consists of tables of consecutive columns which surrounded the consecutive order of magnitude of their unique number system.
It is known that Egyptians uses pebbles to help them count properly. But archaeologists were able to find very old disks of different sizes that resemble an Abacus which could have been used as an easier alternative to help them count properly.
Sometime around 6000 BC, during the time of Achaemenid Persian Empire, Persians has started to use Abacus as they share and adapt different knowledge and invention with their surrounding countries like Rome, India and China.
The earliest archaeological evidence found that proves Greek also used the Abacus was dated back to the fifth century BC. Their Abacus were made of wood or marble and preset with petite counters in wood or metal for their proper calculations. It is believed that Greek saw the use of Abacus from Persians, Etruscan, Rome, and French before they started to adapt it into their lifestyle.
These are just some of the countries that have started to use Abacus in ancient times after the Chinese have invented it. Other countries that are also believed that have a history of using the Abacus are Rome, India, Japan and Korea.