Heavy bombardment and fierce fighting continue to shake the Syrian city of Raqqa, as the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group defend their stronghold from advancing US-backed forces.

Bursts of gunfire and artillery as well as the thud of air attacks conducted by the US-led coalition filled the air in western neighbourhoods of Raqqa on Monday, in what AFP news agency described as the heaviest day of bombardment to date.

The US-backed Syrian Democratic Forces (SDF) said 11 ISIL fighters had been killed in the clashes since Sunday, while the ISIL-linked Aamaq news agency said 14 SDF fighters were killed in the fighting in Raqqa on Sunday alone.

READ MORE: US-led air attacks 'killed 224' civilians in Raqqa

As the fighting continues, thick pillars of black smoke dotted the city skyline, lined with bombed-out concrete homes and the damaged minaret of a mosque.

"Our American friends are bombing with mortars," an SDF fighter told AFP after a string of blasts near the front line in western Raqqa.

The Kurdish-led group has been pressing an operation to capture ISIL's stronghold since last year with coalition air support and the backing of a US Marines artillery battery.

AFP reported that US coalition forces at a joint position with SDF fighters, in Jazra suburb on the western outskirts of the city, have been firing artillery in the direction of ISIL posts deeper inside Raqqa.

"The operation is continuing, but there are many fierce clashes," an SDF spokesman named Ahmed said, speaking in the town of Ain Issa, 50km north of Raqqa.

"We are taking steady and sound steps. What is important to us is not speed, but liberating civilians and eliminating Daesh [ISIL]."

The Britain-based Syrian Observatory Observatory for Human Rights also reported progress in the Old City's southwestern neighbourhood, adding that an estimated 35 percent of Raqqa is now under SDF control.

'Thousands still trapped'

Progress inside Raqqa has been hampered by extensive mining of neighbourhoods, which has slowed advancing SDF fighters and had devastating consequences for civilians trying to flee.

The intensification of fighting comes a week after Iraqi forces declared victory against ISIL in the Iraqi city of Mosul, the largest stronghold the fighters have held.

The loss of Raqqa would deal a major blow to ISIL, but the group still holds wide areas of the eastern Syrian province of Deir Az Zor, bordering Iraq.

The Kurdish-run Hawar news agency said some 180 civilians were able to flee areas controlled by ISIL, while the Observatory put the number in the hundreds.

Observatory director Rami Abdel Rahman said a steady stream of civilians was fleeing ISIL-held districts.

"Whenever there is a lull in the fighting, they leave towards areas held by the SDF," he said.

The SDF on its social media accounts said Monday its forces "managed to free about 500 civilians who were trapped inside the Al-Daraiya and Al-Tayar neighbourhoods, as well as 150 others from the Old City" inside Raqqa.

The United Nations estimates that up to 50,000 civilians remain trapped inside the city, down from some 100,000 people at the end of June.

The SDF began an operation to capture Raqqa in November 2016 and spent months taking territory around the city before finally entering it.

More than 330,000 people have been killed in Syria since the conflict began with anti-government protests in March 2011.