Iraqi Prime Minister Haider al-Abadi has announced the start of a military operation to retake Falluja from so-called Islamic State (IS).

"Zero hour for the liberation of Falluja has arrived. The moment of great victory has drawn near and Daesh has no choice but to flee," he said.

Iraq's military has already warned civilians to leave the town.

Falluja was the first city to fall to IS in 2014 and is one of only two of its remaining strongholds in Iraq.

The Iraqi military told state TV that those who could not flee should raise a white flag above their homes.

The military, police and volunteer fighters virtually surround the city, about 65 km (40 miles) west of Baghdad.

The Baghdad-based pro-Kurdish news website Shafaq said on Sunday that close to 20,000 police troops had arrived on the outskirts of Falluja ahead of the expected assault.

The BBC's Middle East correspondent, Jim Muir, said between 60,000-90,000 civilians remained in Falluja. Many of them are family members of IS fighters, he said.

IS militants launched a sweeping offensive in June 2014 that overran large areas north and west of Baghdad, but security forces and allied fighters have pushed the jihadists back with support from US-led air strikes.

Iraq's military seized the nearby city of Ramadi from Islamic State in December.

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 amount is also dwindling.

Last month, the United Nations and Human Rights Watch warned civilians still living in Falluja were in danger of starvation.

The World Food Programme said stocks were dwindling as government forces trying to recapture the city had cut supply routes, and IS had stopped people from leaving.

Some residents were eating grass to survive, HRW said.

One report in Vox.com said that a 110lb (50kg) bag of flour, which costs about $7.50 in the US, had been sold for as much as $4,166 (£2,925; €3,650).