Special forces on Thursday advanced into the Karama and Quds neighborhoods, while army troops and federal police gained ground in nearby Intisar, Salam and Sumor neighborhoods.
"This is the second phase of the operation to liberate Mosul conducted by the special forces, the federal police and us on this front," General Nejm Jabouri, a senior army commander, told Reuters.
Army troops and allied fighters launched the long-awaited offensive to retake Mosul nine weeks ago. Since then, they have retaken a quarter of the city but their advance has been slow in the face of fierce ISIS resistance.
The battle for Mosul involves 100,000 Iraqi troops, members of the Kurdish security forces and Shia volunteers and is the biggest ground operation in Iraq since the US invasion of the country in 2003.
Daesh terrorists, who took the city in 2014 when they overran large areas north and west of Baghdad, have executed scores of residents in recent weeks, accusing them of collaboration with government troops.
The militants are currently isolated inside the eastern bank of Mosul, military spokesman Yahia Rassol told state television on Thursday.
"In the coming days, Iraqi forces will liberate the entire left bank of Mosul and after that we will tackle the right," he said.
A senior officer said counter-terrorism forces are now less than three kilometers from the Tigris River which slices the city in half. The elite force is conducting the major part of the operation inside Mosul, with other troops remaining outside the city so far.
The operation for liberation of Mosul was initially scheduled to end by the end of 2016 but Prime Minister Haider al-Abadi said Tuesday it would take another three months to retake the city.
The troops have faced grueling urban fighting, often house to house against Daesh militants. Even in districts that have been recaptured, Iraqi troops have faced surprise attacks, shelling and car bombs. The extremists have launched more than 900 car bombs against Iraqi troops in and around Mosul.
Defeating ISIS in Mosul would be a crushing blow to the Takfiri group and probably spell the end for its ambition to rule over millions of people in a self-styled caliphate.
The operation has been slowed by concern to avoid casualties among civilians, who have mostly stayed in their homes rather than fleeing as was initially expected, Press TV reported.
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