They recaptured "Al-Milayeen neighbourhood and Al-Binaa al-Jahiz area and raised the Iraqi flag over the buildings", the military said in a statement.
"These are the last neighbourhoods of the centre of the city (on) the left bank," the statement said, referring to eastern Mosul.
He also said that federal forces had retaken control of the road linking Mosul, Iraq's second city, to Dohuk, a provincial capital in the west of the autonomous region of Kurdistan.
Abadi and top commanders in the Counter-Terrorism Service which has spearheaded operations inside the city had already declared the eastern side of the city "liberated" on Wednesday.
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The Joint Operations Command coordinating the battle against IS in Iraq had said then that a few more days would be needed to clear the last pockets of holdout jihadists.
Iraq's top brass and its foreign allies were expected to confer in the coming days on the strategy to adopt to conquer the west bank of Mosul, which is still under full IS control.
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