Some 3,700 people have fled Falluja, west of Baghdad, over the past week since the Iraqi army began its offensive on the city controlled by militant forces, it said.
"UNHCR has received reports of casualities among civilians in the city centre of Falluja due to heavy shelling, including 7 members of one family on the 28th of May (Saturday)," UNHCR spokesman William Spindler told a news briefing.
"There are also reports of several hundred families being used as human shields by ISIL in the centre of Falluja."
The accounts come from displaced people who have spoken to UNHCR field staff, spokeswoman Ariane Rummery said.
"Most people able to get out come from the outskirts of Falluja. For some time militants have been controlling movements, we know civilians have been prevented from fleeing. There are also reports from people who left in recent days that they are being required to move with ISIL within Falluja," she told Reuters.
Islamic State militants fought back vigorously overnight and parried an onslaught by the Iraqi army on a southern district of Falluja, officers said.
Iraqi authorities are holding some 500 men and boys under the age of 12 for "security screening" as they leave the city, a clearance process that can take up to seven days, Spindler said.
"But people are being released after this process and we understand that 27 men were released yesterday (Monday) after being screened," he said.