Tens of thousands of civilians in parts of Mosul held by Daesh are struggling to get food, water and medicine, the United Nations said, days into a new push by U.S.-backed Iraqi government troops to take the northern city.

Up to 200,000 people still live behind Islamic State lines in Mosul's Old City and three other districts, U.N. Humanitarian Coordinator Lise Grande told Reuters late on Sunday. She spoke a day after Iraq's army said it had launched a new offensive to take the militant zones on the western side of the Tigris river.

Progress has been slow, an Iraqi government adviser told Reuters, also late on Sunday. "The fighting is extremely intense ... the presence of civilians means we have to be very cautious," he said, speaking on condition of anonymity. People who had managed to get out of the militant areas "report a dramatic situation including lack of food, limited water and severe shortages of medicines," Grande said by phone.

"We know that there have been health facilities in these areas, but we don't know whether they are still functioning."

Government forces have been dropping leaflets over the districts telling families to flee - but many have remained fearing getting caught in the cross-fire.

"We have been informed by authorities that the evacuation is not compulsory ... If civilians decide to stay ... they will be protected by Iraqi security forces," said Grande.

"People who choose to flee will be directed to safe routes. The location of these will change depending on which areas are under attack and dynamics on the battlefield," she added. The latest Iraqi government push is part of a broader offensive in Mosul, now in its eighth month. It has taken longer than planned as the militants are dug in among civilians, retaliating with suicide car and motorbike bombs, booby traps, snipers and mortar fire.

When Daesh captured Mosul back in 2014, the Iraqi government faced criticism for being unable to defend one of its largest cities. The oil-rich city fell to Daesh easily as the Iraqi troops avoided clash and fled posts, abandoning their weapons. Today, several groups are cooperating on the ground, but primarily due to international pressure and the U.S. handling of military operations. Interestingly, they had exist during Mosul's fall too, as the Iraqi army unlike other regular armed forces, consisted of several armed groups with different ethnic and sectarian backgrounds and it is a known fact that these groups do not like each other. The battle, however, will not probably end soon and its costs, especially the humanitarian one, will increase. On average, some 4,000 civilians have fled the city every day and 176,000 people in total have been displaced since the Mosul offensive began, the United Nations said.