US-backed fighters in Syria say they have removed Islamic State of Iraq and the Levant (ISIL, also known as ISIS) from Raqqa's Old City, bringing them closer than ever to the armed group's most well-defended positions.

"Our forces today seized full control of the Old City in Raqqa after clashes with Daesh," Talal Sello, a spokesman for the Kurdish-led Syrian Democratic Forces (SDF), told AFP news agency on Friday, using the Arabic acronym for ISIL.

READ MORE: Syria's civil war explained from the beginning

Sello said the SDF was now on the edges of ISIL's "security quarter in the city centre, where most of its main bases are".

Most of ISIL's fighters and up to 25,000 civilians are believed to still be holed up in the city centre.

The SDF, a coalition of Kurdish and Arab fighters, first broke into Raqqa in early June and penetrated its Old City a month later.

They were able to enter it after US-led coalition air raids opened up two gaps in the Rafiqah wall, a 2,500-metre barrier surrounding the Old City.

The SDF has captured more than 60 percent of Raqqa city and most of the surrounding northern province.

Along with the Old City, the SDF also captured the neighbourhood of al-Dir'iya, according to Mustapha Bali, another spokesman for the alliance.

"This victory is a present to our people. The greatest present will be the complete liberation of Raqqa city," he said in a statement.

'Moral victory'

Sello declined to say when the alliance expected to seize all of Raqqa, but said operations were proceeding "according to schedule".

"Control over the Old City - which has historical importance - is a moral victory against ISIL, which is collapsing in Raqqa. Its defeat there is inevitable," he added.

READ MORE: What is left of ISIL's 'caliphate'?

The Syrian Observatory for Human Rights, a Britain-based monitoring group tracking developments in the country's war via a network of contacts on the ground, said the SDF was still locked in clashes with ISIL in a small part of the Old City.

UN sees ISIL defeat by October

Meanwhile, UN Syria envoy Staffan de Mistura said separately on Friday that ISIL's last remaining Syrian strongholds are likely to fall by the end of October.

"What we are seeing is, in my opinion, the beginning of the end of this war ... what we need to make sure is that this becomes also the beginning of peace," he told the BBC.

The US and the US-backed SDF "will probably liberate Raqqa by the end of October", he said, adding that "the Syrian government and the Russians are very likely between now and the end of this month or perhaps early October, latest, to actually liberate [Deir Az Zor]".

ISIL overran Raqqa in 2014, turning it into the de-facto capital of its self-declared "caliphate".

The city was the scene of some of the group's worst atrocities, including public beheadings.