Islamic State fighters halted an Iraqi army assault on the city of Fallujah with a counter-attack at its southern gates.
Meanwhile, the United Nations warned that civilians trapped in the city could be used by militants as human shields.
The Iraqi army's assault on Fallujah has begun what is expected to be one of the biggest battles ever fought against Islamic State, with the government backed by world powers including the United States and Iran, and determined to win back the first major Iraqi city that fell to the group in 2014.
A week after Baghdad announced the start of the assault, its troops advanced in large numbers into the city limits for the first time on Monday, pouring into rural territory on its southern outskirts but stopping short of the main built-up area.
Baghdad describes the assault to retake the city as a potential turning point in its US-backed campaign to defeat the ultra-hardline Sunni Muslim militants who rule a self-proclaimed caliphate across much of Iraq and Syria.
Fallujah, where US troops fought the biggest battles of their own 2003-2011 occupation against Islamic State's precursors, is the militants' closest bastion to Baghdad, believed to be the base from which they have waged a campaign of suicide bombings on the capital less than an hour's drive away.
Retaking it would give the government control of the main population centres in the fertile Euphrates River valley west of the capital for the first time in more than two years.
But the assault is also a test of the army's ability to capture territory while protecting civilians. Although most of Fallujah's population is believed to have fled during six months of siege, 50,000 people are still thought to be trapped inside with limited access to food, water or healthcare.
The United Nations said there were reports that the militants were using several hundred families as human shields in the city centre, a tactic they have employed in other locations in Iraq. It said 3,700 people had managed to escape the city in the past week.
For some time militants have been controlling movements, we know civilians have been prevented from fleeing," said Ariane Rummery, spokeswoman for UN refugee agency UNHCR.
"There are also reports from people who left in recent days that they are being required to move with ISIL within Fallujah," she said, using an acronym for Islamic State, also known as ISIS or Daesh.
Soldiers from Iraq's 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.
A staff member of Fallujah's main hospital said it received reports of 32 civilians killed on Monday.
Medical sources had reported that the death toll in the city stood at about 50, with 30 civilians dead and 20 militants dead, during the first week of the offensive which had yet to involve street fighting.
