The consistent advance - more than two weeks since the new push started to clear Mosul's western side of IS militants - has been a major blow to the extremists who once controlled almost a third of Iraq.
Fighting is expected to get tougher as Iraqi troops push further into the more densely populated areas, including Mosul's old city.
Initial advances in Mosul's western neighborhoods have been slow as Iraqi forces try to conduct simultaneous operations that force ISIS to spread out its defenses.
The location of Baghdadi can not be confirmed but if United States and Iraqi intelligence sources are to be believed, Baghdadi has fled and abandoned the Mosul city.
Photo Credit: null If chemical weapons are used, he said, there is evidence of people injured and material left on the ground but "we don't have anything from the operation in Mosul that tells us we have that".
"We fear it could all collapse at any time", said archaeologist Layla Salihto The Sun. This has meant house to house fighting at a snail's pace, which is why the eastern Mosul offensive took some three months.
The Syrian Democratic Forces (SDF), an alliance including the Kurdish YPG militia, is the main US partner in the war against Islamic State in Syria.
Three weeks ago, USA -backed Iraqi forces launched an offensive to retake the western part of Mosul from ISIS. Losing Mosul would deal a fatal blow to Islamic State's hold over territory in Iraq.
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IS overran large areas north and west of Baghdad in 2014, but Iraqi forces backed by US-led air strikes and other support have since retaken most of the territory they lost.
In Syria the coalition is backing an Arab-Kurdish alliance known as the Syrian Democratic Forces (SDF) that is pushing towards the jihadists' de facto capital Raqa.
Since then, sporadic Islamic State statements mention attacks carried out by suicide bombers at various locations in Iraq and Syria, but place no particular emphasis on Mosul, despite the city being the main center of fighting.
IS had captured Tikrit during its blitz across Iraq in the summer of 2014 when the Sunni militant group seized almost a third of the country's territory.
But one such raid on Tuesday, to retake a government complex, turned into a deadly trap as Islamic State militants from hidden sniper positions fired on Iraqi forces, and previously concealed vehicle bombs rammed their convoys, The Associated Press reported.
An Iraqi commander said the Iraqi Counter Terrorism Service raised Iraq's flag over buildings in the neighborhoods.
Neither al-Baghdadi nor any of his close aides released any comment on the fall of the eastern part of the city in January.
"Those messages in the textbook help them divide the world in two", Feldman said.