A U.S. backed Syrian coalition of Kurdish and Arab groups have made advances into Raqqa the de facto capital of the so-called Islamic State group.
IS has suffered a series of setbacks in recent months at the hands of an array of Syrian and Iraqi forces.
"Since the offensive began, the SDF have captured around 25 percent of the city's built-up neighbourhoods", Rami Abdel Rahman, head of the Syrian Observatory for Human Rights, told AFP on Monday.
Cihan Shekh Ehmed, a spokeswoman for the USA -backed militia known as the Syrian Democratic Forces, said the group's fighters seized the western district of al-Qadisiya from IS on Monday.
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From those neighbourhoods, they were bearing down on Raqqa's Old City in a pincer movement on Monday, with fighting raging in the western al-Qadisiya district and parts of the city's east.
The battle for Raqa is the SDF's flagship offensive, with heavy backing from coalition air strikes, advisers, weapons and equipment.
The report of the gains comes on the same day that US -led Iraqi government troops reported major advances against IS in Mosul, the group's capital in Iraq and its last stronghold in that country.
It became infamous as the scene of some of the group's worst atrocities, including public beheadings, and is thought to have been a hub for planning attacks overseas.
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