Syrian government warplanes took to the skies again Saturday over the flashpoint northeastern city of Hasakeh, despite a US warning against new strikes that might endanger its military advisers.

In another escalation of the five-year war, regime planes this week bombarded positions held by US-backed Kurdish forces in the city fighting the Islamic State (IS) jihadist group.

Turkish Prime Minister Binali Yildirim said the raids showed Damascus was starting to see the Kurdish attempt to consolidate territory in northern Syria as "a threat".

He pledged to play a "more active" in the next months in putting an end to the conflict.

Ankara sees Syrian Kurdish militia as an offshoot of the outlawed Kurdistan Workers' Party (PKK) that has waged a bloody campaign against the Turkish state since 1984.

The unprecedented strikes prompted the US-led coalition to scramble aircraft to protect its special operations forces helping the Kurdish fighters.

It was apparently the first time the coalition scrambled jets in response to regime action, and possibly the closest call yet in terms of Syrian forces wounding American or coalition advisers.

Regime warplanes were in the air above Hasakeh throughout the night and into Saturday morning, according to the Syrian Observatory for Human Rights, a Britain-based monitoring group.

It was unclear whether the aircraft had carried out bombing runs.

- 'Right of self-defence' -

Fighting erupted between pro-government militia and the US-backed Kurdish forces on Wednesday and continued into Saturday morning, leaving a total of 41 people dead including 25 civilians, the Observatory said.

A delegation of Russian officials from the coastal Hmeimim military airport arrived in Qamishli to the north to hold talks between the two sides, a senior Syrian government source told AFP.

A journalist in Hasakeh said on Saturday afternoon that the clashes had abated.

Around two-thirds of the city is controlled by Kurdish forces, while the rest is held by pro-government militia.

The regime and Kurdish forces share a common enemy in IS, but there have been tensions between them in Hasakeh.

The vitriol between the two sides escalated Saturday, as the Kurdish People's Protection Units (YPG) pledged to "protect areas from the terrorism of the regime."

And in an apparent concession to Ankara, a Syrian military statement and Hasakeh's governor began referring to Kurdish security forces for the first time as the PKK, which has taken up arms against the Turkish government seeking an independent state for Kurds.

Thursday's government raids were the first time the regime bombarded Kurdish positions from the air.

Washington's decision to scramble its fighter jets "was done as a measure to protect coalition forces," Pentagon spokesman Captain Jeff Davis said.

"We will ensure their safety and the Syrian regime would be well-advised not to do things that place them at risk," he said, stressing that the US has the "inherent right of self-defence."

- Air strikes 'a message' -

The coalition is conducting additional air patrols in the area after US advisers were moved to a safe location without suffering any casualties, Davis said.

The Observatory said thousands of inhabitants had begun to flee the city, where bread was running out and electricity has been cut.

A government source in Hasakeh told AFP that the air strikes were "a message to the Kurds that they should stop this sort of demand," after Kurds called for the dissolution of a pro-regime militia.

Washington regards the YPG as the most effective force against IS in Syria and has provided them with air support as well as the military advisers.

US special operations forces were based around six kilometres (nearly four miles) north of Hasakeh and reinforcements arrived Friday "from inside and outside Syria, accompanied by military helicopters", Abdel Rahman said.

Separately, two Russian ships in the Mediterranean launched long-range cruise missiles for the first time since December against jihadist targets in Syria on Friday, the Russian defence ministry said.

The targets were linked to the former Al-Nusra Front, now Fateh al-Sham Front, it said.

More than 290,000 people have been killed since the conflict erupted in March 2011.

A surge in violence in Syria's second city Aleppo has left 333 people dead since July 31, the Observatory said Saturday.

The toll includes 165 killed in opposition fire on the city's government-controlled west, and another 168 in air strikes and bombardment on the rebel-held east.

In central Homs province, 20 civilians including five children died overnight in suspected regime air raids and artillery fire on a cluster of towns and villages, the Observatory said.