It said heavy clashes continued to rock other parts of the neighbourhood, where at least 15 civilians were killed Thursday night in air strikes that hit an internet cafe.
"Many are caught in the crossfire", said UNICEF regional director Geert Cappelaere.
The evening news broadcast on Al-Manar TV, which belongs to the Lebanese militant group Hezbollah, hailed the advance of the pro-government forces, and the Hezbollah fighters embedded with them.
The US-led coalition, including the Kurdish armed units, lets militants of the Islamic State terrorist group leave Raqqa instead of killing them, the commander of Russia's force grouping in Syria, Sergey Surovikin said.
The SDF media department said four local journalists were wounded Friday when an IS mortar landed near them as they made their way toward Al-Meshleb.
He called on all parties to provide safe passage to those wishing to leave the city.
The IS suicide bomber targeted a position of the SDF in the Mashlab neighborhood east of Raqqa.More news: Apple unveils watchOS 4 for Apple Watch with new fitness features
The Kurdish-Arab alliance known as the Syrian Democratic Forces (SDF) broke into Raqqa city's east earlier this week, months after they launched an operation to capture the extremist stronghold.
"However, in the course of their offensive, the government troops were confronted with counteraction from the aviation of the US-led worldwide coalition".
The group said the district had been emptied of its civilian population before the SDF entered, and ISIL had dug defensive trenches and tunnels in the area in a bid to hold off attacking forces. He noted that the United Nations reported on 6 June that 163 bodies of murdered Iraqi men, women and children lay on the streets of the Sheer neighbourhood in western Mosul after being shot and killed by ISIS snipers when they desperately tried to flee to safety.
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.
The shooting down came after another incident earlier Thursday in which coalition forces struck "technical vehicles" advancing towards Al-Tanaf.
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.
Surovikin said the USA -led coalition along with the allied Kurds "collude with the leaders of the IS, who surrender the areas under their control and head to provinces where Syrian government forces operate".