Iraqi forces battled jihadists in west Mosul on Sunday, aiming to build a floating bridge across the Tigris to establish an important supply route linked to the recaptured east bank.

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 group (IS) 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.

"We have moved past a large berm constructed by Daesh (IS) with tunnels underneath," he said, adding that the area was heavily mined and his forces had killed 44 jihadists on Sunday alone.

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.

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 tens of 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.

- Key supply line -

"It is very important because if we take it, engineering units... will be able to throw a bridge across from the left bank so we can move supplies and ammunition from the battle field," he said.

Bridging operations under fire are complex and perilous, but Iraqi forces have been trained by the US military and successfully used that 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 on Sunday but IS was fighting back with suicide car bombs, roadside bombs, snipers and weaponised drones.

The elite Counter-Terrorism Service that has done most of the fighting against IS in Mosul so far entered the western neighbourhood of Al-Maamun on Friday.

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.

- 'Eating bird feed' -

The western side of the city is a little smaller than the east but more densely populated and home to some areas considered traditional jihadist strongholds.

It includes the Old City, where Abu Bakr al-Baghdadi made his only public appearance and proclaimed a "caliphate" in July 2014, and several of Mosul's key landmarks.

Around three quarters of a million people are virtually besieged there, in some cases used as human shields by the IS fighters preparing to defend their last major bastion in the country.

"With the battle to retake western Mosul now in its second week, we are extremely concerned about the 800,000 or so still trapped in some of the most dire conditions," Karl Schembri, spokesman for the Norwegian Refugee Council, told AFP.

Food supplies have dwindled as fast as costs have soared, leaving many on barely a meal a day.

"We're hearing reports of people eating bird feed inside western Mosul as they cannot afford the skyrocketing prices," Schembri said.

Residents and medical workers say that the combined effect of malnutrition and the shortage of drugs is starting to kill the weakest.

The United Nations has planned for an exodus of at least 250,000 people from west Mosul, but in the absence of humanitarian corridors only a few hundred have been able to flee so far.

Around 160,000 are currently displaced as a result of the first phase of the Mosul operation. Iraq has a population of more than three million people who have been displaced by the IS conflict.

Iraq: The battle for Mosul
Baghdad (AFP) Feb 24, 2017 - Iraqi forces entered a west Mosul neighbourhood Friday for the first time since launching a vast offensive to seize the city from the Islamic State jihadist group on October 17, 2016.

Here are key dates:

- The battle begins -

- October 17: Iraqi forces launch an assault to drive IS from Mosul. The jihadists had declared an Islamic "caliphate" there in June 2014 after overrunning much of northern and western Iraq.

Tens of thousands of army, police and counter-terrorism troops are thrown into the long-awaited counter-attack with air and ground support from a US-led coalition.

Kurdish militias also take part in operations north and east of the city.

By late October, the army is within 15 kilometres (10 miles) of Mosul.

- Entering Mosul -

- November 1: The army says it has entered Mosul city for the first time since 2014.

- November 3: IS chief Abu Bakr al-Baghdadi breaks a year-long silence, urging followers to fight to the death for Mosul. The Iraqi advance begins to slow.

- November 13: Iraq says it has recaptured Nimrud, an ancient city southeast of Mosul.

- November 23: Shiite-dominated paramilitary units known as Hashed al-Shaabi say they have cut IS supply lines between Mosul and the jihadists' Syrian stronghold Raqa, 400 kilometres (250 miles) to the west.

- Change of tactics -

- December 29: Government troops end a two-week pause and launch the second part of their assault on east Mosul, with increased coordination and coalition support.

- Tigris River bank -

- January 8: Iraqi units reach the Tigris River that divides Mosul and take up positions near one of the city's five bridges, all now destroyed.

- January 14: Elite Counter-Terrorism Service forces seize Mosul University's sprawling campus.

- East Mosul taken -

- January 18: The head of special forces announces the "liberation" of Mosul's east bank, but sporadic fighting continues for several days.

- January 24: The Joint Operations Command coordinating the fight says the east has been "fully liberated".

- Battle for west begins -

- January 24: As Iraqi forces prepare their assault on Mosul's west, the UN warns that 750,000 civilians there are at "extreme risk" and a quarter of a million Iraqis could flee their homes.

Western Mosul, home to the densely-populated Old City and traditional a jihadist bastion, is expected to offer much stiffer resistance than the east.

- February 19: Iraqi Prime Minister Haider al-Abadi announces the start of the campaign for western Mosul, with Iraqi forces backed by coalition air power and increased support from coalition advisers.

- February 20: New Pentagon chief, James Mattis, makes his first visit to Baghdad as Iraqi forces retake the village of Al-Buseif, overlooking the airport and the south of the city.

- February 24: Iraqi forces seize full control of Mosul airport, at the gateway to the western part of the city, and enter their first west Mosul neighbourhood.