BAGHDAD - A leading international relief organization has appealed for more medical assistance to cope with the increasing numbers of civilians fleeing the intensified fighting between Iraqi government forces and the Islamic State group in western Mosul.

Backed by U.S.-led international coalition, Iraqi forces launched an operation in February to drive IS from the western half of Iraq's second-largest city, after declaring eastern Mosul "fully liberated" the previous month. The city is divided by the Tigris River into a western and eastern half and the entire operation to liberate Mosul of the extremists began last October.

But unlike the eastern side, the flow of civilians from the western half has been bigger, given the densely populated areas and intensified house-by-house fighting in old alleys.

In a statement issued late Wednesday, Doctors Without Borders, also known by its French acronym MSF, put the number of civilians fleeing western Mosul in "tens of thousands." MSF said many of those who escaped had bullet wounds or have suffered blasts and shells injuries.

It depicted a grim picture of a lack in medical resources and the inability of ambulances to cope with the number of trauma victims and the long distances needed to transfer patients outside the city for further treatment.

"The need for emergency medical care has risen drastically," said Dr. Isabelle Defourny, MSF director of operations. "We have teams working around the clock treating men, women and children injured by bullets, blasts and shells. Other life-threatening emergencies also need a rapid medical response, such as for pregnant women in need of a C-section."

MSF medical teams in a field trauma hospital, set up when the new push in western Mosul began, have received more than 915 patients, according to the statement. Of those, 763 suffered war-related trauma, 190 of whom needed urgent lifesaving surgery.

More than half of the wounded were women or children under the age of 15, it said.

"The situation is really intense," said an MSF surgeon, Dr. Reginald Moreels. "Every case we receive in the operating theatre is severe, and almost every day we have to deal with mass casualties."

"They are all putting their life at risk to flee a city under siege," he added.

Citing accounts from those who fled western Mosul, MSF said residents still trapped in their houses are enduing lack of infant formula, food and clean water, and warned that conditions "are expected to worsen now that supply routes to the area have been cut off."

The aid group added that its teams have started to see children from western Mosul with severe malnutrition.

Ahmed Sami, a spokesman for MSF-Iraq, said Thursday that the overall number of wounded from western Mosul could be much higher since the aid group only reported those it treated.

Among those who safely reached the government-controlled area was Alaa Saad Abdul-Rahman, a 27-year old father of two who decided to flee with his extended family when the fighting intensified in their Risala neighbourhood.

The family used a hole in a back wall of a neighbour's house that IS militants had used to get to the back street.

"We fled through that hole" once IS fighters had retreated from the area, he told The Associated Press. "We started walking as clashes were still underway."

While making their getaway, the family saw "an old woman gunned down in front of us," Abdul-Rahman said. "Some started to scream and cry. ... I didn't know what to do, whether to run with my kids or stay with my mother and wife."

He described the long hours on that journey as "very scary."

"We were expecting death at any moment," Abdul-Rahman said, speaking to the AP from a relative's house in the government-controlled neighbourhood of Tell al-Ruman inside Mosul.

When they reached safety, he said he burst into tears.