The Syrian Democratic Forces alliance of Kurdish and Arab fighters began the battle for the city earlier this week after seven months of fighting to surround the jihadist stronghold.
Yesterday, an AFP journalist entered the city with SDF fighters and witnessed heavy clashes in the Al-Meshleb neighbourhood, with IS firing multiple mortar rounds towards the advancing forces.
He said part of the neighbourhood was under SDF control but US-led coalition planes were still carrying out strikes against IS fighters elsewhere in the district, one of the largest in Raqa.
The SDF did not allow journalists to return to the city today where fighting was continuing.
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"Our troops are advancing in Al-Meshleb and control parts of it," SDF spokesman Talal Sello told AFP.
"The international coalition forces are working with use on the ground in the battle for Raqa in a highly effective manner," he added.
The US-led coalition said it had carried out 22 strikes near Raqa on Wednesday, hitting IS fighting positions and vehicles as well as a weapons cache and a training camp.
"IS has snipers monitoring Al-Meshleb neighbourhood and has laid mines extensively throughout it," the Observatory said.
The group said the district had been emptied of its civilian population before the SDF entered, and IS had dug defensive trenches and tunnels in the area in a bid to hold off attacking forces.
Fighting was also continuing on the western outskirts of the city, the monitor said, adding that US special forces were actively participating in battles on several fronts.
Yesterday, an AFP correspondent saw coalition armoured vehicles parked among olive trees in the desert east of Raqa, covered with camouflage fabric.
SDF male and female commanders, dressed in fatigues and sporting colourful printed scarves wrapped around their heads, pored over maps on tablet devices to pinpoint targets.
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 abroad.
An estimated 300,000 civilians were believed to have been living under IS rule in Raqa, including 80,000 displaced from other parts of Syria.