Iraqi government security forces and allied militias continued their assault on the Islamic State-held town of Fallujah on Wednesday, killing more civilians than militants in the process, according to sources inside the city.

At least 21 civilians have been killed in the three day-old offensive, compared with 14 Islamic State fighters, a Fallujah hospital source told Reuters.

VICE News was unable to independently verify the numbers.

Aid agencies have become alarmed about civilian suffering in a city that has been under siege for six months, and the United Nations has urged combatants to protect inhabitants trying to escape the fighting.

On Wednesday morning Iraqi troops concentrated artillery fire on Fallujah's northern and northeastern neighborhoods, according to a resident Reuters contacted via the Internet.

The Norwegian Refugee Council (NRC) warned on Tuesday that up to 50,000 people may still be trapped inside the town of 100,000.

"There are thousands trapped in Fallujah with intense fighting raging on their doorsteps," said NRC's country director in Iraq, Nasr Muflahi, in a statement. "Families who have been suffering food and medical shortages over the last months now risk being caught in the crossfire and it is absolutely vital that they are granted safe routes out of there so that we can assist them. All parties to this conflict have to provide safe exits for civilians."

The chairman of Fallujah's local council, Isa al-Isawi, told the Associated Press that around 600 people had managed to escape the city.

"It is not going to be an easy fighting at all," Isawi said from a refugee camp outside the city. "We heard from people who escaped from the city how ISIS militants are prepared for this battle. Peaceful locals are the only victims of this fighting."

"I'm afraid ISIS is going to use [Fallujah residents] as human shields to prevent the Iraqi forces from retaking the city," he said.

Iraq's top Shiite Muslim cleric also urged government forces to spare civilians trapped in the city on Baghdad's western approaches, and which fell to the Islamic State in January 2014.

Grand Ayatollah Ali al-Sistani's appeal reflected concerns that a large civilian death toll in the battle for the mainly Sunni Muslim city could aggravate sectarian tensions in Iraq. The Baghdad government has been led by Shiites since the 2003 fall of Saddam Hussein, a member of the Sunni minority.

"Sayyid Sistani reaffirms his recommendations that the ethics of jihad (Islamic holy war or struggle) be respected," his representative, Sheikh Abdul Mahdi al-Karbalai, said in a statement.

"Don't be extreme... don't be treacherous. Don't kill an old man, nor a boy, nor a woman. Don't cut a tree unless you have to," he said, citing sayings of the Prophet Mohammed.

The offensive is part of a government campaign to roll back Islamic State's seizure of wide tracts of northern and western Iraq. Baghdad's forces retook Ramadi, the Anbar provincial capital near Fallujah, in December but have not yet tackled a bigger challenge — IS-held Mosul, Iraq's largest northern city.

An Iraqi military spokesman said troops were trying to tighten the encirclement of Fallujah by advancing on the western front, near the village of Khalidiya.

The Association of Muslim Scholars of Iraq, a hardline political organization formed after Saddam's ouster to represent Sunnis, has condemned the assault on Fallujah as "an unjust aggression, a reflection of the vengeful spirit that the forces of evil harbor against this city."

Sistani wields enormous influence over Iraq's Shiites. It was at his call that Shiite militias regrouped in 2014 in a coalition known as Hashid Shaabi (Popular Mobilization), to stem Islamic State's stunning advance through the north and west.

Hashid Shaabi will take part in encircling Fallujah but will not enter the city unless the Iraqi army fails in doing so, said Hadi al-Amiri, the leader of the Badr Organisation, the largest component of the Shiite coalition.

"Our decision is to encircle the city from the outside and let the security forces operate; if the security forces are unable to cleanse the city, we will then go in,'' he said, according to video recording on the state-run TV channel.

The US-led coalition is providing air support to the Iraqi government security forces, and said it had attacked an IS tactical unit and destroyed one of the group's vehicle and a front end loader.