Ground and air units are patrolling near the Syrian border town of Darbasiya.
The blast on Saturday ripped through a crowded market in Tal Abyad, a town controlled by Turkish-backed opposition fighters.
“Based on first findings, 13 civilians were killed and around 20 others injured” in the explosion, Turkey’s defence ministry said in a statement.
The northeastern town has witnessed some of the heaviest fighting since the Turkish military launched an operation in northeast Syria last month against the Syrian Democratic Forces (SDF), which is spearheaded by the Kurdish People’s Protection Units (YPG) and was for years allied to the United States in the fight against the Islamic State of Iraq and the Levant (ISIL or ISIS) armed group.
An AFP news agency correspondent in Tal Abyad saw the skeletons of two motorbikes ablaze in the middle of a rubble-strewn street.
A group of men carried the severely burned body of a victim onto the back of a pickup truck, as a veiled young woman stood aghast by the side of the street.
The Syrian Observatory for Human Rights said pro-Turkey fighters and civilians were among the dead and wounded in the car explosion.
“We condemn this inhuman attack of the bloody PKK/YPG terrorists who attacked the innocent civilians of Tal Abyad who returned to their homes and lands as a result of the Operation Peace Spring,” Turkey’s defence ministry said on Twitter.
No group has yet taken responsibility for the attack.
The Turkey-based Kurdistan Workers Party (PKK) is designated a terrorist group by Ankara and its Western allies. The PKK launched a separatist rebellion against the Turkish state in 1984.
Ankara considers the YPG a terrorist group because of its ties to PKK rebels in southeast Turkey.
On October 9, days after US President Donald Trump’s abrupt decision to pull out US troops from northeast Syria, Turkey and allied Syrian rebels launched the cross-border operation and seized control of Tal Abyad and some 120km (75 miles) of land along the frontier.
Turkey says the goal of the offensive was to carve out a “safe zone” cleared of the Kurdish fighters and repatriate some of the 3.6 million refugees currently residing on its soil.
On Friday, Turkish and Russian troops in armoured vehicles held their first joint ground patrols in northeast Syria under a deal between the two countries that forced the YPG away from territory near Turkey’s border.
According to the agreement, Ankara will control a 32km-wide (20 miles) area between the towns of Tal Abyad and Ras al-Ain, which covers 120km (75 miles) of the Turkish-Syrian border.