There has been no official comment from Ankara although at least one Turkish official Tweeted that the slain people had been fighters with the YPG militia.
Fighting over the weekend continued in other parts of Syria.
The clashes underscore the complexity of the US -led worldwide coalition campaign to reverse Islamic State's territorial hold in Syria and the dangers faced in that mission. Targeting the Kurdish forces also could fuel friction with Washington, which views the SDF and the YPG as its most effective partners against the Islamic State.
Ankara wants to force the Kurds to withdraw to the east of Euphrates River, stopping short of establishing a corridor to link two Kurdish-held areas in northwestern Syria, the BBC said.
Violence between the PKK (Kurdistan Workers' Party) and the security forces resumed last year, after the collapse of a two-year peace process in July.
The latest fighting is likely to raise deep concerns for Turkey's North Atlantic Treaty Organisation ally the United States, which supports the Kurdish militia - known as the People's Protection Units (YPG) - as an effective fighting force against IS.
Turkey launched the cross-border offensive on Wednesday to support the FSA in its fight against terror group DAESH.
A Turkish army convoy drive from the border back to their base in Karkamis on the Turkish-Syrian border in the southeastern Gaziantep province, Turkey, August 27, 2016.
The Jarablus Military Council group, which is allied to the SDF, said a Turkish air strike in the village of al-Amarna caused civilian casualties and called it "a unsafe escalation that threatens the fate of the region". U.S. State Department spokesman John Kirby said in March that the U.S. does not consider the PYD or the YPG to be terrorist organizations.
On Saturday, one Turkish soldier was said to have been killed by Kurdish group attack near Jarablus. It didn't give any more details about the location of the attack.
BBC reports that a monitoring group claims at least 35 civilians and four militants are killed by a wave of Turkish strikes in the same area.
Aleppo24 said that at least 28 civilians died in Turkish airstrikes, including people in Amarneh and a family from the neighboring village of Saressat.
The fighting killed 20 civilians in Jub al-Kousa and 15 in al-Amarna, while scores more were wounded, the group said.
A Reuters witness in Karkamis, a Turkish border town, heard jets and artillery bomb Syrian targets.
Turkey has suffered shock waves from the conflict raging in its southern neighbor, including bombings by Islamic State.
Thomas Grove and Yeliz Candimir in Istanbul and Raja Abdulrahim and Noam Raydan contributed to this article.