Machine gun fire and shelling could be heard while smoke arose from one part of Bab al-Kheir, a town near the Turkish border, Reuters reported.
Probable casualties and damage resulting from the clashes in the town have yet to be confirmed.
The civilians were killed following Turkish airstrikes on Bab al-Kheir which lies east of Ras al-Ayn, according to Rami Abdel Rahman, head of the so-called Syrian Observatory for Human Rights.
The reports come only 13 hours after Turkey agreed to "pause" the assault for five days allowing Kurdish fighters to withdraw from a determined "safe zone" north of Syria.
The Turkish capital hosted more than five hours of negotiations between a US delegation and Turkey's President Recep Tayyip Erdogan earlier in the day.
US Vice President Mike Pence told reporters on Thursday that Ankara’s incursion "will be halted entirely on completion" of the withdrawal of the fighters.
Certain details regarding the withdrawal, however, appear to be disputed between the parties to the agreement.
Pence has said that the deal obliges Turkey to not engage in military operations in the Syrian border town of Ayn al-Arab, also known as Kobani. Turkish Foreign Minister Mevlut Cavusoglu has, however, said Ankara has made no commitments about the town.
Also speaking on Thursday, Mazlum Abdi, commander of the Syrian Democratic Forces which leads Kurdish-led forces in the region, told a Kurdish TV station that the group would accept the deal but that it was limited to the border areas running between Ras al-Ayn and the town of Tal Abyad.
Turkey launched its invasion of Syria on October 9 with the alleged aim of creating a "safe zone" south of its border with Syria.
Ankara says Kurdish forces operating in the area are terrorists linked to the homegrown Kurdistan Workers' Party (PKK) militant group, which has been seeking an autonomous Kurdish region in Turkey since 1984.
Speaking earlier on Thursday, however, Syrian President Bashar al-Assad dismissed Ankara's announced objectives in Syria.
“No matter what false slogans could be made up for the Turkish offensive, it is a flagrant invasion and aggression,” he said.