Islamic State militants fought back vigorously overnight against an onslaught by the Iraqi army on a southern district of the city of Falluja, the group's bastion near Baghdad, officers said on Tuesday.
Soldiers from the elite Rapid Response Team stopped their advance overnight about 500 metres from the al-Shuhada district, the southeastern part of city's main built-up area, an army commander and a police officer said.
"Our forces came under heavy fire, they are well dug in in trenches and tunnels,'' said the commander speaking in Camp Tariq, the rear army base south of Falluja, 50 km west of Baghdad.
A staff member of Falluja's main hospital said they received reports of 32 civilians killed on Monday. The toll could not be confirmed by a second source.
Medical sources in the city had reported that the death toll in the city stood at about 50, 30 civilians and 20 militants, during the first week the offensive which started on May 23.
Falluja has been under siege for more than six months. Foreign aid organisation are not present in the city, but are providing help to those who manage to exit and reach refugee camps.
The latest offensive is causing alarm among these organisations as more than 50,000 civilians remain trapped with limited access to water, food and health care.
Falluja is the second-largest Iraqi city still under control of the militants, after Mosul, their de facto capital in the north that had a pre-war population of about 2mn.
Prime Minister Haider al-Abadi announced the assault on Falluja on May 22 after a spate of bombings that killed more than 150 people in one week in Baghdad, the worst death toll so far this year. A series of bombings claimed by Islamic State also hit Baghdad on Monday, killing over 20 people.
Falluja has been a bastion of the insurgency that fought both the US occupation of Iraq and the Baghdad government that took over after the fall of dictator Saddam Hussein, in 2003.
It was the first city to fall under Islamic State control, in January 2014.