Russia's Ministry of Defense reported on Friday that pro-government forces circled around US military advisers in eastern Syria to reach the Iraqi border, dealing what could be a major blow to the declared USA mission to defeat Islamic State militants in the desert region.
Its regional spokesman David Swanson said as many as 100,000 people "may stay trapped" inside during the assault.
SDF fighters were armed mostly with light weapons including Kalashnikovs, and were also returning mortar fire on IS positions.
US-backed fighters battled ISIL on Thursday as they tried to push further into the extremists' Syrian bastion Raqqa, two days after finally entering the northern city. They are expected to progress from the district into neighbouring Al-Senaa and the Observatory said some of the overnight strikes targeted the area between the two districts.
Surovikin also said that aviation of the US-led worldwide coalition is impeding the struggle of the Syrian government forces against terrorists.
"Hundreds" of United States military personnel are taking part in the Raqqa offensive, according to the Pentagon, which said Thursday it believed up to 2,500 extremists were still holed up in Raqqa.
The International Rescue Committee said it was "deeply concerned for the safety of civilians in Raqa" after a drop in numbers fleeing the city in the past week.
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The SDF - an Arab-Kurdish alliance formed in 2015 - launched its campaign to capture Raqa in November and chipped away at IS territory around the city's north, west, and east.
"We are accompanying SDF units moving in Raqa", he said, but "the SDF have the lead in the fight".
Along with Mosul in Iraq, Raqa was one of the twin pivots of the self-styled Islamic "caliphate" that Daesh declared almost three years ago.
"Our forces liberated a large factory of sugar in addition to a strategic military base used by Daesh [IS] and previously belonging to the Syrian army", she said.
The US-led coalition said it had carried out 22 strikes near Raqqa on Wednesday, hitting ISIL fighting positions and vehicles as well as a weapons cache and a training camp.
The U.S. has dealt the Syrian government and its allied troops several blows near Tanf close to the border with Jordan, where the U.S. trains Syrian opposition forces.
It was the second time in less than a month that the coalition had attacked pro-regime forces that strayed too near to the garrison.