Civilians have been warned by the Iraq military to flee Fallujah or raise white flags above their homes as they prepare a major assault on the city held by the Islamic State (IS).
Fallujah was the first city in Iraq to fall to the group in January 2014, and is one of only two of its remaining strongholds in Iraq.
Iraq's military told state television said those who could not leave should raise a white flag above their homes, as the the military, police and volunteer fighters virtually surround the city.
The forces around Fallujah have been heavily reinforced in preparation for the assault on several fronts that military sources say could begin in the next day or so, and which they expect to to last two or three weeks.
The Baghdad-based pro-Kurdish news website Shafaq said on Sunday (local time) that close to 20,000 police troops had arrived on the outskirts of Fallujah
The BBC's Middle East correspondent, Jim Muir, said between 60,000 and 90,000 civilians remained in Fallujah, which is about 50km west of Baghdad. 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.
Mr Muir said the two or three week timeframe may be optimistic, given the many weeks it took earlier this year to take full control of Ramadi, another city further to the west.
Fallujah has been held by the militants of IS much longer - 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 Fallujah will be a lot less tough than it was for Ramadi.
Should IS lose Fallujah, it would leave the northern city of Mosul, Iraq's second-largest city, as its only Iraqi stronghold. It continued to hold large parts of territory in neighbouring Syria, though that area was also dwindling.
Last month, the United Nations and Human Rights Watch (HRW) warned civilians still living in Fallujah 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.