Tehran (AFP) - Key Damascus supporter Tehran urged Ankara on Wednesday to quickly wrap up its week-old military intervention in Syria, saying it was an "unacceptable" violation of Syrian sovereignty.

Turkey's cross-border offensive, which it says is aimed against US-backed Kurdish militia as well as the Islamic State jihadist group, marks the first major ground intervention by a foreign power carried out without the blessing of Damascus.

"In the fight against terrorism, any resort to methods that cast a shadow over the political sovereignty and legitimate power of the central government is unacceptable," Iranian foreign ministry spokesman Bahram Ghasemi said.

"Although the fight against terrorism... is a principle for all peace-seeking governments, it cannot and must not justify military operations on another country's territory without coordination with its central government."

Tehran has long had military advisers and volunteers on the ground in Syria in support of the regime, while Moscow has deployed special forces, artillery and warplanes.

Washington too has special forces on the ground advising its Kurdish militia allies in their fight against IS.

But Turkey's deployment is far bigger. Its troops and tanks are accompanied by Syrian rebels that it has long supported in their fight against the regime and its Iranian and Russian allies.

After driving IS out of the border town of Jarabulus, Ankara quickly turned its sights on the US-backed Kurdish militia, who control territory to the south, pounding them with deadly shelling and air strikes to the dismay of Washington.

Ankara regards the Kurdish People's Protection Units (YPG) as an extension of the outlawed Kurdistan Workers Party (PKK) it has been fighting in southeastern Turkey for three decades.

A senior US military official said on Tuesday that Washington had brokered a "loose agreement" between the two sides for an end to the fighting.

But on Wednesday Turkish EU Affairs Minister Omer Celik said Ankara did not accept a ceasefire with the Kurds.

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The Iranian spokesman said that until Turkey pulled out, the conflict would only intensify.

"The Turkish army must quickly stop its military operations," he said.

"Any escalation of the conflicts in northern Syria will lead to the killing of more innocent civilians."