An Iranian-backed Shia Iraqi militia said on Saturday it planned to storm Fallujah, Islamic State (IS) group's stronghold near Baghdad, once civilians left the city, backtracking on earlier statements that it would leave this task to the Iraqi army.

"We will not enter Fallujah as long as there are families inside," said Hadi al-Amiri, leader of the Badr Organization, the largest component of the Shia paramilitary coalition known as Hashid Shaabi, or Popular Mobilization.

"Of course, we will go in and rid the city from the evil of this cancerous gland, with nobody preventing us," he said, when asked what would happen if civilians managed to flee the Sunni city that lies 50 km (32 miles) west of Baghdad.

Fallujah is the first Iraqi city that IS group captured, in January 2014, and the second largest still under its control after Mosul in the north. Sunni politicians have voiced concern that the presence of Shia militias alongside the army in the battle to retake the city could lead to sectarian violence.

Amiri was speaking to reporters while touring one of the frontlines near Fallujah. Last week he said the militias would take part in encirclement operations but leave the army to storm the city.

Prime Minister Haider al-Abadi said on June 1 the offensive to dislodge the ultra-hardline Sunni militants had slowed down in order to protect civilians. About 50,000 are trapped in the city, with limited access to water, food and healthcare, according to the United Nations.

Fallujah is a historic bastion of the insurgency against the US occupation of Iraq and the Shia-led authorities who took over after the overthrow of Saddam Hussein, a Sunni, in 2003.