U.S.-backed Syrian forces have advanced into opposite sides of Islamic State's so-called Syrian capital of Raqqa, the forces and a war monitor said on Saturday.

The Syrian Democratic Forces (SDF), a group of Kurdish and Arab militias supported by a U.S.-led coalition, began to attack Raqqa on Tuesday after a months-long campaign to cut it off.

The U.S.-led coalition estimates that Raqqa, which Islamic State seized from Syrian rebels in 2014 during their lightning advance in Syria and Iraq, is defended by 3,000-4,000 jihadists.

It has been a hub both for Islamic State's military leaders and its bureaucrats, and has been used to plot attacks in countries around the world.

The SDF said it had seized al-Mishlab district in the far east of Raqqa on Friday and al-Sabahia district in the west. The war monitor, the Syrian Observatory for Human Rights, said the SDF had taken Mishlab and more than half of Sabahia.

The forces are now advancing into al-Romania district in northwest Raqqa, the SDF and the Observatory said. Islamic State had turned back an earlier SDF assault on a military base on the north side, the Observatory said.

Islamic State still has a long sweep of territory along Syria's Euphrates valley and wide stretches of desert, despite recent losses to the SDF, the Syrian army and rebel groups.

To the west of Raqqa, the Syrian army and its allies have advanced into Islamic State territory and on Friday reached SDF lines near the town of Tabqa, 40 km from the city.

The Syrian government has described the SDF's war against Islamic State as “legitimate” and said its military priorities are further east, suggesting it does not plan to confront the group now.