Quoting local sources, Turkey's state-run Anatolia news agency on Tuesday said the security forces fired shots at Kurdish crowds commemorating the killing of 5000 people in a 1998 chemical weapons attack in neighbouring northern Iraq.
It said three people were killed in the city of Aleppo and four in the town of Afrin. The sources said those killed were Kurds.
But in a statement issued by its embassy in Paris, Syria strongly denied any suggestion of inter-ethnic tension and blamed the violence on politically motivated "troublemakers".
A senior official in Syria said two people were killed in a clash between Kurdish and Arab tribes over an old vendetta in Ras al-Ain near the border with Turkey, but denied reports of other clashes.
Syria's cabinet said in a statement that those who broke the law would be punished.
There are about two million Kurds in Syria's 17 million population, of whom 200,000 are not recognised as citizens.
Syria has been witness to violence between Arabs and Kurds in recent days, triggered last Friday by a football match in the town of Kameshli.
Kurdish groups have accused the Syrian authorities of anti-Kurd bias. The Human Rights Association of Syria has also alleged that the authorities have arrested hundreds of Kurds in recent days.
Syrian officials avoid reference to Kurds as a distinct minority and stress the importance of national unity. Kurds and other minorities have held senior government and army positions.