Syrian government fighter jets have bombed Kurdish-held areas of the northeastern city of Hasakah for the first time in the five-year-old civil war, according to fighters and a monitoring group.

The Kurdish People's Protection Units (YPG), a key US ally in the fight against the Islamic State of Iraq and the Levant (ISIL) group, said on Thursday that it would "not be silent" over what it called it an act of aggression.

There was no immediate comment from the Syrian government.

YPG spokesman Redur Xelil said that the air raids had hit Kurdish districts of Hasakah and positions held by a Kurdish security force known as the Asayish.

"There are martyrs and wounded," he told the Reuters news agency.

Government forces were also bombarding Kurdish districts of Hasakah with artillery, and there were fierce clashes in the city, which is mostly controlled by Kurdish groups..

"Every hand spattered with the blood of our people will be held to account through all possible and available means," the YPG said in a statement.

READ MORE: The YPG - America's new best friend?

The UK-based Syrian Observatory for Human Rights, which tracks the war using a network of activists, said jets had targeted Kurdish security forces' positions in the northwest and northeast of Hasakah.

It also said that there was fighting in several parts of the city.

The Syrian government, which routinely uses its air force against rebels fighting President Bashar al-Assad in western Syria, still has footholds in Hasakah and Qamishli, both in the Hasakah governorate.

The latest bout of fighting is the most significant between YPG and government forces since several days of battles in Qamishli in April.

The YPG makes up a significant portion of the US-backed Syria Democratic Forces (SDF), a Kurdish and Arab alliance fighting ISIL in Syria.

Last week the SDF, backed by air raids from a US-led anti-ISIL coalition, said they had pushed ISIL fighters from the city of Manbij near the Turkish border after a two-month campaign.

Syria's complex, multi-sided war has created a patchwork of areas across the country controlled by the government, rebels, Kurdish forces or ISIL.

Kurdish groups have exploited the collapse of state control to establish autonomy across much of the north.