The fighters have also entered Raqqa's western neighborhood of Sabahiya and the industrial district in the east.
Even with assistance from USA military advisors and air support, it has taken Iraqi forces nine months of prolonged combat to reach Mosul's Old City.
"We are moving carefully and cautiously to avoid the huge number of mines that Daesh has planted in the city", the source added.
This undated frame grab from video posted online Sunday, June 10, 2017, by the Aamaq News Agency, a media arm of the Islamic State group, shows damage caused by bombardment by the US -led coalition and USA -backed fighters in the northern Syrian city of Raqqa.
It has since turned into war pitting extremists, rebel groups, government forces, and Kurdish fighters against each other.
The hate preacher, who has a $25million bounty on his head, had been believed to be hiding out in the desert outside the besieged city of Mosul in northern Iraq.
But outside factors, including ongoing tensions between the USA and Turkey over the Kurdish role in the operation, ultimately hindered efforts to speed up the Raqqa assault.
Baghdadi moves in ordinary cars, or the kind of pick-up trucks used by farmers, between hideouts on both sides of the Iraqi-Syrian border, with just a driver and two bodyguards, said Hashimi. A week into the operation to liberate Raqqa, questions over the true strategic importance of the city have only grown louder within defense and national security circles.
At the height of its power two years ago, Islamic State ruled over millions of people in territory running from northern Syria through towns and villages along the Tigris and Euphrates river valleys to the outskirts of the Iraqi capital Baghdad.
A source told Xinhua that there is no direct coordination between the SDF and the Syrian army, adding that there seems to be a plan between the USA and Russian Federation regarding the roles of each force in the battle for Raqqa.
The city has always been seen as a prize by multiple parties to the Syrian conflict, including the government, Russia, Turkey and the US-led coalition bombing IS since 2014.
Since March, the regime has carried out offensives in Deir Hafer, an Islamic State enclave 30 miles east of Aleppo, and al-Bab.
The Kurdish-led SDF seized control of the Science Collage building of Raqqa University. Nor has there been any response from the US-led coalition force.
"Most of the terrorist organizations, especially ISIS, have decentralized their command and controls, but the reality is that he was the central figure of that", Schreiber said. The Syrian Democratic Forces do not coordinate their activities with the Syrian Army.
He is the leader of the terrorist organization, Islamic State of Iraq and the Levant (ISIL).