Cross-border fire killed three others in the city of Mardin's Nusaybin district, some 200 kilometres to the east of Sanliurfa, according to an official statement.
Twenty-four were injured in Mardin, local broadcasters including CNN Turk reported.
The United Nations said tens of thousands of civilians were fleeing Turkey's "Operation Peace Spring" in the east of the Euphrates River. The offensive threatened an escalation of the world's largest displacement crisis, the UN added.
A group of 14 aid agencies warned that around 450,000 people living within 5 kilometres of the Syria-Turkey border are at risk. Some vital services have been interrupted, including medical facilities and water supplies, the groups said.
Turkish forces and their allies were  engaged in heavy fighting with Kurdish fighters late Thursday on the outskirts of Ras al-Ain, Kurdish sources said.
They said that Turkish forces under cover of heavy shelling had tried to infiltrate Ras al-Ain, but the Kurdish-led Syrian Democratic Forces (SDF) forces had foiled the attempt.
The Kurdish Red Crescent said Turkish shelling on Qamishli and Tal Abyad had killed seven people on Thursday, among them a child, and wounded more than 25 other people.
Syria's director general of antiquities, Mahmoud Hammoud, announced that Turkish shelling had affected archaeological sites in north-eastern Syria dating back to thousands of years, particularly in the Qamishli and Tal Abyad areas.
Ankara has been criticized by Western allies, with the EU calling on Ankara to stop the offensive.
President Recep Tayyip Erdogan lashed out at international critics.
"Hey European Union! Pull yourself together. If you describe our current operation as an act of invasion, it is easy - we will open the gates and send 3.6 million refugees your way," Erdogan told his ruling Justice and Development Party (AKP) in the capital, Ankara.
Turkish armed forces have "neutralized" 109 "terrorists," Erdogan said, adding that Ankara wants to avert the creation of a "terrorist state" along its borders.
Erdogan was referring to members of the Kurdish-led Syrian Democratic Forces (SDF), which Turkey views as terrorists threatening its border security.
The SDF controls large areas in north-eastern Syria and has been Washington's main partner in defeating the Islamic State terrorist group.
Many nations are concerned that the attack on the SDF could lead to a revival of the Islamic State. French President Emmanuel Macron said the offensive runs "the risk of helping Daesh [Islamic State] rebuild a caliphate."
US President Donald Trump, who paved the way for the offensive by pulling out some troops and abandoning Syrian Kurdish fighters, said Turkey would have to take care of the Islamic State threat.
Erdogan said Turkey will keep some of the Islamic State captives in prison and will send others back to their countries of origin "if they are accepted."
The United Nations Security Council met on Thursday behind closed doors to discuss the incursion, but the members failed to agree on any steps forward.
European nations voiced concern that a new conflict in the region would lead to further instability, humanitarian crises and refugee outflows.
On Friday, NATO Secretary General Jens Stoltenberg will meet Turkish President Recep Tayyip Erdogan and Foreign Minister Mevlut Cavusoglu in Istanbul.
German Foreign Minister Heiko Maas communicated his country's concerns to Cavusoglu, saying Berlin and Brussels feared "major negative consequences up to a revival of Islamic State."
France and Italy summoned the Turkish ambassadors in protest of the offensive.
Arab League foreign ministers plan to hold a crisis meeting on Saturday on a request from Egypt.
Erdogan lashed out at Egypt and Saudi Arabia, charging the latter was killing civilians in Yemen. "Saudi Arabia should look in the mirror. You have destroyed Yemen."
Israeli Prime Minister Benjamin Netanyahu warned "against the ethnic cleansing of the Kurds by Turkey and its proxies."
The Syrian government sharply criticized the incursion, calling Erdogan "an imprudent killer," the state news agency SANA reported.
----------------------------------------------------------------------------------------------------------