Violence was reported from the city of Aleppo, where at least two civilians were killed in rocket fire. Many residents fled their homes as the clashes intensified. At least 15 people were reported injured, according to Syria's state news agency Sana.
The Syrian government's defense minister called for a ceasefire late Monday, while representatives of the Kurdish forces, known as the SDF, also urged their fighters not to respond to attacks.
According to the SDF, one woman was killed and 17 people were injured.
It is unclear what led to the clashes, and both sides accuse the other party of opening fire first.
The unrest broke out at the same time that Turkish Foreign Minister Hakan Fidan was in Damascus for talks about, among other things, how the Kurdish militant groups should be incorporated into Syria's military.
Fidan met with the Syrian transitional government's Foreign Minister Asaad al-Shaibani. The agenda also included joint efforts to combat the terrorist movement ISIS and Israel's military attacks in southern Syria.
Stability in Syria means stability in Turkey, Fidan said at a joint appearance, and then accused the Kurdish SDF of countering positive developments in Syria.
