Three quarters of a million civilians living in west Mosul are at "extreme risk", the United Nations warned Tuesday as Iraqi forces prepared for a push into the jihadist bastion.

A hundred days into a massive offensive to retake the Islamic State group's last major stronghold in Iraq, federal forces and jihadists took up positions on either side of the Tigris River that divides Mosul.

The three months it took to reconquer Mosul's east saw some tough fighting, but even deadlier battles are expected on its west bank, which is home to the narrow streets of the Old City and some of IS's traditional redoubts.

"We hope that everything is done to protect the hundreds of thousands of people who are across the river in the west," the United Nations' humanitarian coordinator for Iraq, Lise Grande, said in a statement.

"We know that they are at extreme risk and we fear for their lives."

Iraqi forces have retaken all central neighbourhoods in east Mosul, and on Tuesday were clearing Rashidiyah, which lies on the northern edge of the city and is the east bank's last area still to be secured.

Tens of thousands of other security personnel are deployed north, south and west of Mosul, meaning that the jihadists are trapped in the city where their leader Abu Bakr al-Baghdadi proclaimed his "caliphate" in 2014.

Residents of west Mosul and civil activists told AFP on Monday that IS fighters had forced civilians along the riverfront to leave their shops and homes.

- Bridges bombed -

"The group forced us to leave our homes... without allowing us to take our belongings," a resident of Al-Maidan said. "It deployed gun positions and posted snipers on roofs and at windows."

Facing them across the river are some of Iraq's most seasoned elite forces, whose engineers some reports said were already working on assembling pontoon bridges for a cross-river assault.

All bridges across the Tigris in Mosul were either bombed by IS or hit by air strikes carried out by the US-led coalition that has helped Iraq reclaim about two thirds of the territory it lost to IS in 2014.

"The Iraqi forces have over the course of their battle against Daesh (IS) in this country developed the capability to do bridging, including bridging while under fire," coalition spokesman Colonel John Dorrian said.

The coalition has meanwhile sought to prevent IS from moving on the Tigris, destroying more than 100 boats in the Mosul area over a period of six days, it said.

The UN had feared an exodus of unprecedented proportions before the Mosul offensive began on October 17, but while 180,000 people did flee their homes, the majority stayed.

It now estimates that 750,000 people still live in Mosul's west bank, either because they did not want to leave their homes or were prevented from doing so by IS, which has routinely used civilians as human shields in this conflict.

"We don't know what will happen in western Mosul but we cannot rule out the possibility of siege-like conditions or a mass exodus," Grande said in the statement.

- Death blow -

"To date, nearly half of all the casualties from Mosul are civilians. It's terrifying to think of the risks families are facing," she said.

The Norwegian Refugee Council, which assists some of the displaced families, also said the lack of access to west Mosul was a source of great concern, given the humanitarian crisis that fighting in the east had already caused.

"Those still trapped inside Mosul city are in even graver danger due to the fighting and shortages and, 100 days since the fighting started, we still have no way to reach them," it said in a statement.

The recapture of Mosul by Iraqi forces would deal a death blow to the Iraqi part of IS's caliphate, with the next major target the group's stronghold of Raqa in neighbouring Syria.

In retaken areas of eastern Mosul, efforts to resume a normal life picked up in recent days, with many shops reopening and children starting to go back to school.

The UN Children's Fund said 30 schools had reopened this week.

"After the nightmare of the past two years, this is a pivotal moment for the children of Mosul to reclaim their education and their hope for a better future," UNICEF's Iraq representative Peter Hawkins said.

The UN said more than 20,000 people displaced since the Mosul offensive began have already returned to their homes in areas retaken from IS.