The US-backed Kurdish-Arab alliance fighting to wrest the Syrian city of Raqa from the Islamic State group was engaged Monday in its toughest fighting yet, a spokeswoman said.

"The Syrian Democratic Forces are currently waging their toughest battles yet," said Jihan Sheikh Ahmed, spokeswoman for the operation launched in early June to retake IS's one-time de facto Syrian capital.

An estimated 300 diehard jihadists holding no more than 10 percent of the eastern city were bracing for a bloody last stand after the weekend evacuation of most civilians set the stage for the SDF's final assault.

The latest fighting "will bring an end to Daesh's presence, meaning they can choose between surrendering and dying," Sheikh Ahmed told AFP, using an Arabic acronym for IS.

The jihadists are trapped and the outcome of the battle is in no doubt but flushing out a group of mostly foreign fighters who have nothing to lose and who had months to prepare remains a perilous task.

"The IS elements that are still there are resisting," the spokeswoman said, adding that the neighbourhoods where fighting is under way "are fortified and heavily mined areas