A tank of Iraqi rapid response forces fires against Islamic State militants at the Bab al-Tob area in Mosul on Monday.
Iraqi forces launched a campaign to recapture Mosul from Islamic State in October.
They expected to gain control of the Iron Bridge and the nearby area by the end of the day, he said.
Another operation to retake the Iron Bridge bridge in Old City near the Tigris river resulted in the death of Daesh military commander Abu Abdul Rahman al-Ansary.
The army had earlier recaptured the east of the city in an offensive that began previous year.
The coup marks a significant strategic victory as the bridge connects the eastern part of Mosul, which has been entirely freed of terrorists' presence, to the city's Daesh-held Old City.
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Iraqi forces said Monday that they have taken more territory from jihadists and were searching for militants and bombs on the edge of the Old City as they press an offensive in west Mosul.
Soldiers from the 9th Armored Division scored an important victory on Saturday night when they cut the last road out of west Mosul, said Brett McGurk, the USA envoy to the worldwide anti-IS coalition.
"We now believe that we are killing so many of their fighters that they are not able to replace them".
Displaced Iraqis stand in front of a destroyed building to get into Hamam al-Alil camp on Tuesday..
"Daesh wanted us to move to their areas but we escaped when the army arrived", he said.
More than 65,000 of them fled their homes over the past two weeks, the organisation said.
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U.S. envoy Brett McGurk said on Sunday that the remaining western Mosul neighbourhoods held by ISIL were surrounded and the group had lost more than 60 percent of the territory it once held in Iraq.
Until the latest phase of the battle to take western Mosul, the campaign had gone well with lower-than-expected civilian losses, Khanjar said crediting the professionalism of the US trained elite forces.
Mainstream Sunnis believe the Shi'ite led administration has discriminated against them and also say Shi'ite Iran's influence has expanded in the security forces and paramilitary groups.
Almost 100,000 people have been displaced by the battle to retake west Mosul from IS.
"Whenever we advance there are more people coming out", said one Iraqi officer directing refugee transport.
In practice, IS fighters may still be able to sneak in and out of the city in small numbers, but the lack of access to roads makes larger-scale movement and resupply more hard, if not impossible.
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Losing the city would be a huge blow to Islamic State as it has served as the group's de facto capital since its leader Abu Bakr al-Baghdadi proclaimed himself head of a caliphate spanning Iraq and Syria from the Nuri Mosque in July 2014.