The SDF entered Raqa in early June, after months of fighting to encircle the city with support from the US-led coalition against IS.
The militia "controls 70 per cent of Raqa after taking the Al-Thakana district in the centre of the city," said Rami Abdel Rahman, director of the Syrian Observatory for Human Rights monitor.
"The advance was made possible by violent clashes and heavy air strikes by the international coalition," he told AFP.
"The end of fighting will be dictated by the international coalition. Air power will be the main, determining factor."
The fierce fighting has pushed civilians to flee away from the frontline into remaining IS-held areas in the north of the city, the monitor said.
Tens of thousands of people have fled the fighting since the SDF offensive began.
The UN estimates up to 25,000 people could remain trapped in the city, though the Observatory said the number is now fewer than 10,000.
The monitor said "a few hundred" jihadists remain in the city, adding that the SDF was continuing to sustain losses, with IS using mines and snipers to target the attacking force.
More than 330,000 people have been killed in Syria since the conflict began with anti-government protests in March 2011 before spiralling into a brutal civil war that has drawn in international players.
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