The Britain-based Syrian Observatory for Human Rights said SDF fighters now control Romaniah and the eastern neighbourhood of Mashlab.
With support from US airstrikes, the SDF secured Raqqa's western district of al-Romaniah and the eastern neighborhood of al-Meshleb. The ISIS leader "was said to have been wounded after a US-led coalition bombing raid in Al-Ba'aj in northern Iraq", reported the Sun.
"Daesh is shooting anyone who sticks their head out", one SDF fighter said.
Located 90 miles from Raqqa, where US -backed militias began their assault to retake the city last week, the fertile stretch of land along the banks of the Euphrates River is home to Madan, Deir el-Zour and other Islamic State redoubts.
On January 6, 2014, fierce fighting between the rival groups ended when Daesh's predecessor seized control of the city.
Captured by the jihadists in 2014, Raqa has become synonymous with IS atrocities including beheadings and public displays of bodies, and also emerged as a hub for planning attacks overseas.
In October 2016, Amnesty International said it had received "credible witness and photographic evidence" that Iraqi and coalition forces had deployed white phosphorus near the Iraqi village of Karemlesh, which is 20 miles from the city of Mosul.
After repeated assaults, the SDF seized parts of the heavily fortified Division 17 military base as well as all of an adjacent sugar factory, the Observatory said.
The UN estimates there are about 230,000 civilians living in Raqqa city.
Since the offensive began, the SDF, supported by heavy coalition airstrikes, has taken territory to the west, east and north of the city.
Thousands have fled in recent months, and the United Nations humanitarian office estimates that about 160,000 people remain in the city.
We sent several questions to Operation Inherent Resolve, the U.S. Joint Task Force which heads an global coalition fighting the Islamic State in Iraq and Syria, but we did not receive a response in time for publication.
Raqqa is Being Slaughtered Silently, an activist group in Raqqa, said coalition air strikes have destroyed several buildings, including schools and mosques, in the past week.