A member of the Iraqi security forces fires artillery during clashes with Isis militants near Fallujah, Iraq, 29 May, 2016 Reuters
The Iraqi army has started an operation to storm Fallujah,
where around 50,000 civilians are trapped in Isis's stronghold near Baghdad.
Troops backed by artillery and tanks entered the city from three directions
in the early hours of Monday morning, commanders told the AFP news agency.
A Reuters TV crew reported hearing explosions and gunfire in Fallujah's southern Naimiya district.
"Iraqi forces entered Fallujah under air cover from the international coalition,
the Iraqi air force and army aviation and supported by artillery and tanks,"
Lieutenant General Abdelwahab al-Saadi, the commander in charge of the operation, told reporters.
"Counter-terrorism service (CTS) forces, the Anbar police and the Iraqi army, at around 4am, started moving into Fallujah from three directions," he said.
"There is resistance from Daesh," he added, using the Arabic acronym for Isis.
On Sunday, Iraqi Major Dhia Thamir said troops had recaptured 80 per cent of the territory around Fallujah since the operation began
The Iraqi army, supported by Iranian-backed Shia militia, began the operation to recapture Fallujah on 23 May.
The military warned the between 50,000 and 60,000 civilians trapped insideto get ready to leave before fighting started. The jihadists have been preventing from residents leaving for months.
The Norwegian Refugee Council said around 3,000 people had managed to escape the area this week.
Isis execution squads with orders to kill anybody trying to flee or surrender have appeared in the streets of Fallujah. “Groups of Isis fighters are saying they will kill anybody in Fallujah who leaves their house or waves a white flag,” Ahmed al-Dulaimi, a political activist, reporting from Iraq.
Fallujah, a long-time bastion of Sunni Muslim jihadists, became the first city to fall to Isis in January 2014, six months before the group swept through large parts of Iraq and neighbouring Syria. The extremist group still controls territory in Iraq's north and west, including Mosul, the country's second largest city.
The United Nations and Human Rights Watch said last month that residents of Fallujah were facing acute shortages of food and medicine amid a siege by government forces. Aid has not reached the city since the Iraqi military recaptured nearby Ramadi, the Anbar provincial capital, in December.
Additional reporting by agencies