The Islamic State of Iraq and the Levant (ISIL) group has launched an assault on the largely Kurdish city of Hasakah in northeast Syria, a UK-based monitoring group has said.

Saturday's clashes came a day after Kurdish militia killed 20 civilians accused of supporting ISIL, the Syrian Observatory for Human Rights said.

"ISIL fighters started an assault on Hasakah city and reached the city's southern periphery, where they are clashing with pro-regime forces," said the group's director, Rami Abdelrahman.

He said the pro-government National Defence Forces militia had blocked the ISIL advance on the city's edges and reported heavy shelling.

Syria's official news agency SANA said loyalist forces had "foiled a terrorist attack by ISIL on military points near Hasakah".

Control of Hasakah, capital city of the province by the same name, is split between President Bashar al-Assad's regime and Kurdish forces.

Kurdish forces said they would protect their part of the city but not come to the help of the regime.

"The fighting at this moment is between ISIL and regime forces and we are not part of it. And, for sure we will not take part in it and we will not support the regime forces inside the city," Redur Khalil, spokesperson of the People's Protection Units, told Al Jazeera.

Abdelrahman said at least 10 government loyalists had been killed, but he had no immediate information on ISIL casualties.

Hasakah is home to a mix of ethnic groups, the largest being Kurds, Arabs, and Assyrians.

Homes demolished

The Assyrian Network for Human Rights activist group said ISIL had launched "a new attempt at seizing control of the city" and seized one checkpoint on Hasakah's southwest edges.

"Hasakah has been hit by mortar rounds since Saturday morning," and a local church had been damaged, the Assyrian Network said.

Elsewhere in Hasakah province, Kurdish militia executed at least 20 civilians on Friday, including two children, after accusing them of being ISIL supporters, the Syrian Observatory reported.

The group said Kurdish militia also burned and demolished homes of people it suspected of supporting ISIL near the flashpoint towns of Ras al-Ain and Tal Tamr.

The Kurdish People's Protection Units (YPG) in Hasakah have been battling ISIL fighters over a series of key towns in the province bordering Turkey.