Al-Qaeda-linked militants tightened their grip on Fallujah, a city on Baghdad's doorstep that has been outside of government control for weeks, as bombings in the capital killed 18 people Monday.

The latest violence came as security forces pressed a massive assault on anti-government fighters in Ramadi, another predominantly Sunni Arab city where swathes of territory have been outside of the authorities' control.

And a top official warned that militants had enough weaponry to "occupy Baghdad".

Diplomats have urged Iraq to pursue political reconciliation in order to undercut support for militants, but Prime Minister Nuri al-Maliki and others have taken a hard line and trumpeted security operations.

After days of tense calm in Fallujah, a former insurgent bastion a short drive from Baghdad, tribal chiefs and witnesses said Al-Qaeda-linked militants were increasingly exerting their authority in the city on Monday.

Fighters affiliated with the Islamic State of Iraq and the Levant (ISIL) had set up an Islamic court, kidnapped senior officials including a top police officer and several tribal sheikhs, and broadcast calls over mosque loudspeakers for others to join them in the fight against Iraqi security forces.

"Daash does not accept anything that we decide," said one tribal sheikh, who spoke on condition of anonymity for fear of being targeted by militants, referring to ISIL by its commonly-used Arabic acronym.

"They want everybody to work under their command, under their regime."

Another resident of the city, who gave his name as Abu Osama, said militants had imposed strict codes in some neighbourhoods, including barring women from visiting local markets and men from wearing Western clothes or shaving their beards.

Security forces continued to mount major operations against militants in Ramadi, and in rural areas between the two cities, but the clashes and unrest caused several casualties.

A bombing near Ramadi targeting a group of policemen and media going to ceremonially reopen a police station on Monday killed three people -- two policemen and a journalist -- and wounded three others, including another reporter.

Clashes and bombings in and around Ramadi on Sunday and Monday left two other people dead and 15 others wounded, while security forces said at least seven militants, including a senior ISIL commander, had also died.

'Enough to occupy Baghdad'

Ramadi, where a major security force operation to reclaim militant-held areas of the city entered a second day, and Fallujah were both former insurgent bastions and have staged months of anti-government protests.

Fighters have moved in and taken control of parts of Ramadi and all of Fallujah after recent unrest.

It marks the first time anti-government fighters have exercised such open control since the height of the insurgency that followed the US-led invasion of 2003.

Deputy Interior Minister Adnan al-Assadi warned in a speech on Monday that militant groups fighting in Anbar had amassed "numerous and modern" weapons.

"They are enough to occupy Baghdad," he said. "Their target is not just controlling Fallujah or (the nearby town of) Garma, it is to topple the entire political process."

Deadly violence also struck the capital on Monday, with at least six car bombs ripping through Shiite-majority neighbourhoods, killing 18 people in all, according to security and medical officials.

Baghdad security spokesman Saad Maan, however, said 10 people were killed.

"The explosions target the innocent," said a man who gave his name as Abu Ali, a market stall owner in Baghdad Jadidah, one of the neighbourhoods hit.

"Look here -- everything has been destroyed. Everything I had was in this shop, and now everything has been destroyed."

A nearby restaurant owner, Abu Mohammed, referred to the ubiquitous concrete blast walls across Baghdad and said, "All the streets are closed off by concrete walls, and we still do not know where these car bombs come from."

"This is the second time my restaurant has been hit," he said. "In the first one, I lost my son. Thanks God, this time I did not lose anyone, but my restaurant has been completely destroyed."

No group immediately claimed responsibility for the attacks, but Sunni militants including those linked to Al-Qaeda frequently set off coordinated bombings across the capital.

On Saturday evening, a wave of explosions across Baghdad killed 25 people, while 37 more died in a similar spate of attacks on Wednesday.