A week into a major push on the western side of the city, where an estimated 2,000 holdout jihadists and 750,000 civilians are trapped, government forces made steady progress.
But after relatively easy gains on the city's outskirts, they encountered increasingly stiff resistance from the Islamic State (IS) group defending its emblematic stronghold.
"We had an important operation this morning to move towards the bridge," Colonel Falah al-Wabdan of the interior ministry's Rapid Response units that have spearheaded the breach into west Mosul told AFP in the Jawsaq neighbourhood.
Wabdan was referring to what is known as "the fourth bridge", the southernmost of five bridges -- all of which are damaged and unusable -- across the Tigris River that divides the northern Iraqi city.
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Government forces retook the east bank from IS a month ago, completing a key phase in an offensive on Mosul that began on October 17 and has involved thousands of fighters.
Wabdan said that securing the bank area near the fourth bridge would allow engineering units to extend a ribbon bridge to the other side and further pile pressure on the jihadists.
Bridging operations under fire are complex and perilous, but Iraqi forces have been trained by the US military and successfully used the strategy before in the fight against IS.
A ribbon bridge assembled with US assistance over the Euphrates River was considered a turning point in the battle that eventually saw Iraqi forces retake the western stronghold of Ramadi from the jihadists a year ago.
Rapid Response was confident it could reach the bridge today but IS was fighting back with suicide car bombs, roadside bombs, snipers and weaponised drones.
Troops from the US-led coalition assisting Iraq in its efforts to claw back the swathes of territory it lost to IS in 2014 have stepped up their involvement on the ground in recent weeks.
They are officially deployed in Iraq as trainers and advisers, but have increasingly been drawn into combat and been more visible than ever on the front lines since the push on west Mosul was launched on February 19.