The Syrian Observatory for Human Rights said on Thursday that 10,000s of civil have been forced to flee in the conflict.
The NGO, which is based in the United Kingdom and has a large network of collaborators in the field, said many had left from cities such as Al-Darbasiyah and Ras al-Ayn, which were left almost empty.
Syrian troops and Kurdish militias are fighting in the border areas where Ankara aims to create a "safe zone" to resettle two million Syrian refugees.
The Syrian Democratic Forces, an alliance led by Kurds, said that at least nine people have so far died from Turkish bombing in northern Syria.
Among those killed were two children and one was injured by the bombing of Turkey against the city of Qamishli, one of the most populous cities in the territory controlled by the Kurdosyr and where Damascus also dominates an area, including the airport.
Tell Abyad and Ras al-Ayn are located on the border within the so-called "safe zone" of 30 km that Turkey intends to conquer.
The Turks have already conquered several towns and villages near those two towns, according to the NGO.
Ankara began a ground operation on Tuesday night hours before the air campaign against the border, a territory previously dominated by the Popular Protection Units (YPG), backbone of the SDF, which have de facto established a local administration.
The YPG have been allies of the US so far in the fight against the jihadist group Islamic State, but Ankara considers it a terrorist organization for its links with the banned Kurdistan Workers Party, the active Kurdish guerrilla in Turkey.
The rest of northern Syria, from the Euphrates River to the Mediterranean Sea, is already under the control of Turkish troops, after the Operation Euphrates Shield north of Aleppo in 2016, and Operation Olive Branch in the Kurdish enclave of Afrin in 2018.
( With inputs from IANS )