It said the Iraqi CTS troops took over the neighbourhoods of Malayeen, Samah, Khadra, Karkukli, Quds and Karama.
They raised the Iraqi flag over buildings in those neighborhoods, and inflicted heavy losses on the militant, the statement said.
BHut outside the city's eastern limits, hundreds of civilians streamed away from the conflict, packed into cars, pickups and trucks, waving white flags and hooting horns.
Cows and sheep also filled the road from Kokjali, on the eastern edge of Mosul.
"This town, Kokjali, is cleared. There are a few metres that separate Kokjali from the Karama, Intisar and Sawah neighborhoods. It is very important to secure these locations and to protect civilians," head of the Joint Operations Command, Lieutenant General Talib Shaghati, said.
Fleeing residents said there had been heavy mortar fire launched by retreating ISIS terrorists.
By mid-morning, a Reuters correspondent in Kokjali saw smoke rising from inside Mosul but there were no sounds of fighting.
Earlier on Thursday, ISIS leader Abu Bakr al Baghdadi told his followers there could be no retreat in a "total war" against the forces arrayed against them, as advancing soldiers battled the militants inside their northern Iraqi stronghold.
The battle for Mosul is expected to be the biggest in the 13 years of turmoil unleashed in Iraq by the 2003 US led invasion.
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