The agency quoted Yasser al-Dulaimi, a spokesman for the Anbar police, as saying that the army is continuing its offensive against the jihadists in order to fully regain control of the city.
"Several Daesh ringleaders and the terrorist group's members have fled the remaining areas in Ramadi [and are heading] towards the Soufiya and Sajariya regions in the eastern parts of the city," Yasser al-Dulaimi said.
He pointed to "the intensive and continued attacks of the Iraqi forces, their artillery fire and airstrikes," which he said had prodded Daesh ringleaders to flee the city located in central Iraq's Anbar province, about 110 kilometers (68 miles) west of the capital Baghdad.
FARS also cited Raed Raisan, senior commander of the volunteer forces, as saying that the Iraqi forces had managed to make significant advance in Ramadi after they reached the Tigris River and started entering the city center after crossing al-Khor bridge.
Meanwhile, Ramadi residents have warmly welcomed army troops into the liberated areas of the city, with the army now reportedly heading toward the al-Humaira region south of Ramadi, according to media reports.
Earlier this week, Iraqi Army Chief of Staff Lieutenant General Othman al-Ghanimi said his troops needed only days to completely drive Daesh out of Ramadi, which has been under Daesh control since May 2015.