Kurdish forces in north-eastern Syria called on fighters loyal to Syrian President Bashar al-Assad to lay down their arms and surrender, amid an advance in al-Hassakeh city.

The city has seen heavy clashes over the last week as well as unprecedented airstrikes by al-Assad's forces, who previously enjoyed a tense co-existence with the Kurdish movement that dominates the north-east of the country.

"To all the regime militiamen who are surrounded in the city: You are now in the targets of our forces, snipers and weapons," the Kurdish People's Protection Units (YPG) militia announced by loudspeakers in the city.

Most of al-Hassakeh is dominated by the YPG, but al-Assad's forces and loyalist militias have retained control of the city centre and some mainly Arab areas.

A similar situation prevails in the other main north-eastern city, Qamishli, fuelling charges by the opposition and rebel forces that the YPG is an ally of al-Assad.

Idriss Nassan, a senior Kurdish official, said the YPG had taken control of most of the city's Ghweiran neighbourhood, one of the largest Arab-populated districts and the main government stronghold outside the city centre.

The Syrian Observatory for Human Rights, a monitoring group, said that the Kurds also gained control of al-Hassakeh's central prison in the evening, and now held 90 per cent of the city.

Kurdish and government officials both confirmed that Russian officers were holding talks between the two sides aimed at resolving the conflict.

Russia is a key ally of al-Assad but is also on good terms with the dominant Kurdish Democratic Union Party (PYD). The YPG, widely seen as the PYD's military wing, is also the key US ally on the ground in Syria against the Islamic State extremist group.

A top PYD leader meanwhile drew a link between the clashes in al-Hassakeh and reports of a rapprochement between al-Assad's government and Turkey, a prominent backer of the Syrian opposition and vehement opponent of the Syrian Kurdish forces.

"This is the first time since the liberation of the Kurdish areas ... that the regime air force carries out direct strikes on our positions ... This is related, as I have said, to the rapprochement between the Syrian regime and the Iranian and Turkish regimes," PYD joint president Salih Muslim said.

"Turkey's interest and objective is that the Kurds don't get any democratic rights, whether in ... Rojava [Syrian Kurdistan] or in Turkey," Muslim said in a telephone interview with dpa.

The airstrikes on Kurdish positions in al-Hassakeh were a "kind of positive response" by al-Assad to "courtship" from Ankara, Muslim argued.

There has been speculation that Turkey will shift its policy on Syria after President Recep Tayyip Erdogan recently mended fences with his Russian counterpart Vladimir Putin.

Ankara distrusts the PYD and YPG due to their close links with Kurdistan Workers' Party (PKK) guerrillas operating on its own territory.

Clashes intensified throughout last week between al-Assad loyalists and the Kurdish forces. The US warned the Syrian government not to threaten its allies with warplanes.

The Kurds, who make up about 10 per cent of Syria's pre-war population of 22.4 million, long suffered discrimination under the rule of al-Assad's Baath Party, an Arab nationalist organization.

Since 2012, the PYD has succeeded in gaining control over most Kurdish-populated areas in the north-east and near Aleppo, establishing what it describes as a democratic autonomous administration which it promotes as a model for the rest of the war-torn country.

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