The Iraqi army says it has begun an operation to storm Falluja, a bastion of so-called Islamic State (IS).
It comes a week after the government launched a concerted effort to retake the city, which has been held by the jihadists since 2014.
An estimated 50,000 civilians are trapped inside, with only a few hundred families escaping so far.
As the army pushed on Falluja, a wave of bombings in and around the capital, Baghdad, killed at least 20 people.
State forces including members of an elite counter-terrorism unit are moving into Falluja on several fronts, an official statement said.
IS fighters are reportedly putting up resistance with suicide and car bombings. But while the military said it was advancing towards its goals, so far the fighting seems to be centred on IS defences outside Falluja’s city limits, the BBC’s Jim Muir in Baghdad says. Militia leaders taking part have said there is likely to be a pause before the assault on the city centre begins to allow more civilians to escape.
There is alarm over conditions faced by civilians, with reports of people starving to death and of being killed for refusing to fight for IS.
The Iraqi military has urged those remaining to either leave the city or stay indoors, though IS is preventing civilians from fleeing.
Falluja fell to IS in January 2014, a key moment in its rise that saw it declare a caliphate across swathes of Iraq and Syria.
Along with Mosul, it is one of two major cities held by IS in Iraq.
Meanwhile three districts of Baghdad have been targeted in attacks.
In the worst attack, a car bomb detonated at an army checkpoint in the mainly Shia area of Shaab, killing at least 11 people.
Another suicide attacker targeted Sadr City, a Shia area of Baghdad, killing at least two people.
A suicide bomber struck a market in Tarmiya, a town 50km (30 miles) north of Baghdad, killing at least seven.
All three bombings have been claimed by IS in an online statement.
The group frequently targets Shia Muslims, whom the Sunni militant group regards as apostates.
The attacks may also be an attempt to deflect attention from the operation in Falluja.
