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Falluja assault: Iraq PM announces beginning of military operation
The BBC's Middle East correspondent, Jim Muir, said 60,000 to 90,000 civilians remained in Falluja, many of them family members of IS fighters.
IS militants launched a sweeping offensive in June 2014, overrunning large areas north and west of Baghdad. However, security forces and allied fighters have pushed the jihadists back with support from US-led air strikes.
A former US ambassador to Iraq predicted the Falluja operation would take some time.
"I think Haider al-Abadi has taken the advice of many of his American advisers, which was not to rush into this thing," Christopher Hill told BBC Radio 5 live.
"So they're being very deliberate, very careful, and so I think there's some good reason for optimism that ultimately this will be successful."
Analysis: Jim Muir, BBC News, Baghdad
The Iraqi army, police and irregular forces virtually surround Falluja and have been heavily reinforced in preparation for an assault on several fronts that military sources say could begin in the next day or so, and which they expect to last two or three weeks.
That may be optimistic, given the many weeks it took earlier this year to take full control of Ramadi, another city further to the west.
Falluja has been held by the militants of IS much longer, for nearly two and a half years, and has withstood a massive battering by government shelling and bombing.
But Iraqi military sources believe the number of militants there has been cut roughly in half and that the battle for Falluja will be a lot less tough than it was for Ramadi.
Should IS lose Falluja, it would leave the northern city of Mosul, Iraq's second-largest city, as its only Iraqi stronghold. It continues to hold large parts of territory in neighbouring Syria, though that too is shrinking.