Under siege in the northern city for three months, Daesh 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, Daesh 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.
"This allowed the Syrian Democratic Forces to control 90 percent of the city."
The SDF is an alliance of Kurdish and Arab forces the coalition is backing in Syria with air strikes, equipment and advisers.
Daesh pulled out of the north of the city and abandoned its grain silos and mills, and was now confined to the city centre, Abdel Rahman said.
The SDF said its forces had mounted a "surprise attack" on Daesh in the city's north.
"We consider this the final stages of the Wrath of the Euphrates campaign, which is nearing its end," the statement said.
Daesh seized Raqa in early 2014, transforming the city into the de facto Syrian capital of the "caliphate" it declared after taking control of large parts of Syria and Iraq.
It quickly became synonomous with the group's most gruesome atrocities, including public beheadings, and Daesh 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 Daesh's defensive capabilities.
"After hundreds of their fighters were killed in recent weeks, the remaining Daesh fighters will not be able to resist much longer in Raqa as their military equipment and basic necessities are dwindling," he said.
Without food or medical equipment, Daesh was unable to treat its own wounded and had retreated to the city centre, which it considered "the most secure," he said.
But the battle for the 10 percent of the city still held by Daesh will likely be tough, as the jihadists had heavily mined the area, Abdel Rahman said.
Daesh 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.
AFP journalists on Tuesday saw a military convoy of US-made vehicles, bulldozers, and arms being transported through northeastern Syria.
Syria's conflict broke out in March 2011 with protests against President Bashar al-Assad, but has since evolved into a complex, multi-front war.
More than 330,000 people have been killed and millions have been forced to flee their homes.