ISLAMIC State forces are holding several hundred families as “human shields” in the Iraqi city of Fallujah while government forces close in, the United Nations refugee agency says.

Some 3700 people have fled Fallujah, 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 casualties among civilians in the city centre of Fallujah due to heavy shelling, including seven members of one family on the 28th of May (Saturday),” UNHCR spokesman William Spindler told a news briefing on Tuesday.

“There are also reports of several hundred families being used as human shields by ISIL in the centre of Fallujah.”

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 Fallujah. For some time militants have been controlling movements, we know civilians have been prevented from fleeing,” she said.

“There are also reports from people who left in recent days that they are being required to move with ISIL within Fallujah.”

Thousands of civilians flee raging battle for #Falluja in Iraq https://t.co/UEMDWjSjdu pic.twitter.com/aBXY9pReAP — UN Refugee Agency (@Refugees) May 31, 2016

Islamic State militants fought back vigorously and parried an onslaught by the Iraqi army on a southern district of Fallujah, 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.

Meanwhile, Islamic State has urged Muslims to destroy their satellite TV sets to prevent hostile channels “destroying their beliefs and polluting their ethics”.

The ultra-hard line Sunni group issued its call as military pressure increased against it with offensives targeting its strongholds in Raqqa, Syria, and in Fallujah, west of Baghdad.

“The enemies of Islam are waging a media war on the Islamic State that is no less dangerous than the military campaign,” the group said in a video on its official Telegram account, filmed in Raqqa and monitored in Egypt.

It did not say whether it would try to enforce its appeal in the territory under its control in Syria and Iraq.

It singled out religious channels funded by Saudi Arabia and also showed the logos of Al Jazeera and Orient TV, a channel close to the Syrian opposition, as well as the Egyptian religious channel al-Nas.

The video ended with a scene showing people stamping on satellite dishes to destroy them.

Islamic State declared a caliphate over the territory of Syria and Iraq in 2014.