Iraq's prime minister says relations with northern neighbour Turkey could "not move forward one step" without a withdrawal of Turkish forces from a camp in northern Iraq.

Iraq's state television quoted Haider al-Abadi as making the comments on Tuesday, referring to Turkish forces stationed at Bashiqa camp near Mosul from before the start of an offensive against the Islamic State of Iraq and the Levant (ISIL) group.

Speaking in November, Fikri Isik, Turkey's defence minister, said his country's military involvement was part of its preparation for "important developments in the region".

"Turkey is preparing in advance for whatever happens [and] this is one element of that," he was quoted by the official Anadolu news agency as saying.

Also on Tuesday, Iraqi forces fought their way into more districts of Mosul but advances in the city's southeast were being slowed by ISIL's use of civilians for cover, military officials said.

The UN said civilian casualties had streamed into nearby hospitals in the past two weeks as fighting intensified in ISIL's last major stronghold in Iraq.

Advances by elite forces in the city's east and northeast have picked up speed in a new push since the turn of the year, and US-backed forces have for the first time reached the River Tigris, which bisects the city.

"They entered Hadba [district] today. There is a battle inside the city," Lieutenant-Colonel Abbas al-Azawi, a spokesman for the Iraqi army's 16th division, said.

Seizing control of Hadba, a large district, would likely take more than a day, and ISIL, also known as ISIS, was deploying suicide bombers, Azawi said.

READ MORE: Analysis - What is Turkey trying to achieve in Iraq?

Recapturing Mosul after more than two years of ISIL rule would be a huge blow to the fighters' power in Iraq.

The UN Humanitarian Coordination Office (OCHA) said nearly 700 people had been taken to hospitals in cities in Kurdish-controlled areas outside Mosul in the last week, and more than 817 had required hospital treatment a week earlier.

"Trauma casualties remain extremely high, particularly near frontline areas," OCHA said.

The US-backed operation to drive ISIL fighters from Mosul began in October and has recaptured villages and towns surrounding the city, and most of Mosul's eastern half.