Under siege in the northern city for three months, IS is struggling to defend its one-time bastion under a barrage of air strikes by the US-led coalition battling the jihadists in Syria and Iraq.
"Because of the heavy coalition air strikes, IS withdrew from at least five key neighbourhoods over the past 48 hours," said Rami Abdel Rahman, head of the Britain-based Syrian Observatory for Human Rights.
The SDF is an alliance of Kurdish and Arab forces the coalition is backing in Syria with air strikes, equipment and advisers.
IS pulled out of the north of the city and abandoned its grain silos and mills, Abdel Rahman said.
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It was now confined to the city centre, in government administrative buildings, the stadium and tunnels.
The SDF said its forces had mounted a "surprise attack" on IS in the north of the city.
"We consider this the final stages of the Wrath of the Euphrates campaign, which is nearing its end," a statement said.
It quickly became synonomous with the group's most gruesome atrocities, including public beheadings, and IS is thought to have used the city to plan attacks abroad.
The SDF spent months encircling the city before entering it in June and sealing off all access routes.
Abdel Rahman said the siege had worn down IS's defensive capabilities.
"After hundreds of their fighters were killed in recent weeks, the remaining IS fighters will not be able to resist much longer in Raqa as their military equipment and basic necessities are dwindling," he said.
But the battle for the 10 percent of the city still held by IS is likely to be tough, as the jihadists have heavily mined the area, Abdel Rahman said.
IS has used mines, snipers, car bombs, and weaponised drones against the SDF offensive.
Tens of thousands of civilians have fled the fighting in recent months. Estimates of the number still inside the city range from fewer than 10,000 to as many as 25,000.
"We will continue the campaign until we achieve our aim," Jihan Sheikh Ahmed, the SDF's spokeswoman for the Raqa offensive, told AFP.