A brutal jihadist group has garnered headlines for an Iraq onslaught, but it is actually the leading member of a fragile Sunni coalition including Saddam loyalists and others unified only by a common enemy.

The swift assault, spearheaded by jihadist group the Islamic State of Iraq and the Levant (ISIL), swept down from north Iraq last week, overrunning all of one province and major areas of three others.

ISIL is the major force behind the drive, and has been the focus of international attention, but the onslaught also involves a raft of other groups that have little in common except anger towards Iraq's Shiite-led government.

"ISIL represents the main force that is in control and that is driving things," an officer in Prime Minister Nuri al-Maliki's security office told AFP, speaking on condition of anonymity.

The jihadists are "not letting any other organisation share this leadership," he said.

- Other Sunni Arab groups -

But they are joined by other Sunni Arab groups, such as the Army of the Men of the Naqshbandiyah Order -- known by their Arabic acronym JRTN -- and the Army of Mohammed, "though their role is limited in this attack and there are differences."

JRTN, once cited by US and Iraqi officials as a bigger long-term threat to Iraq's stability than Al-Qaeda, is believed to be close to Izzat Ibrahim al-Duri, who was vice president under ousted dictator Saddam Hussein and the most senior member of his regime still at large.

The Army of Mohammed battled US forces in Fallujah, and was also involved in the insurgent takeover of the city early this year.

"These groups are also receiving logistical support and propaganda and motivation from members of the Baath Party," the officer said, referring to Saddam's otherwise secular party.

There are "ideological difference between (Baathists) and the jihadist organisations, but they are supporting ISIL in this phase because (they think) the enemy of my enemy is my friend," he added.

Members of Ansar al-Sunna, which claimed attacks against American forces, and the Islamic Army, which includes Saddam-era officers, are "also fighting government forces in this attack that the country is now witnessing," military expert Anwar Mahmud Khalaf al-Juburi told AFP.

- 'Coordinating and exchanging information' -

"Even if they differ among themselves, they are coordinating and exchanging information," said Juburi, who was a general in Saddam's army.

Also apparently playing a role are unaffiliated armed tribesmen, whose prominence has risen after Maliki called on Sunni Arab tribal leaders to renounce links to the insurgency.

Toby Dodge, the director of the Middle East Centre at the London School of Economics, said that within the anti-government coalition, "you've got unaligned groups fighting, you've got previous nationalist insurgents, you've got the Naqshabandis, and you've got ISIL."

ISIL is the most powerful militant group in Iraq and a major force in the rebellion across the border against Syrian President Bashar al-Assad.

It has claimed Nineveh, a northern Iraqi province that was the first to fall in the offensive, as part of its Islamic state, and begun imposing its strict interpretation of Islam on residents.

ISIL and its allies have also overrun major areas of three other provinces -- Kirkuk, Salaheddin and Diyala, and pushed to within less than 100 kilometres (60 miles) of Baghdad.

- Request for air strikes -

In a sign of how dire the situation has become, Iraqi Foreign Minister Hoshyar Zebari said on Wednesday that Baghdad has officially requested that Washington carry out air strikes against "terrorist groups".

Iraq's security forces wilted in the face of the initial militant onslaught, in some cases abandoning uniforms and even vehicles to flee.

But they seem to have at least somewhat recovered, and are pushing back against militants with the support of Shiite militiamen.

They will also be joined by thousands of civilians who have volunteered to fight, an effort bolstered by support from top Shiite cleric Grand Ayatollah Ali al-Sistani, who is revered by millions.

Iraqi government efforts to push the militant groups back may ultimately be aided by the militant groups' major ideological differences, said Dodge.

"If history repeats itself, then ISIL, because it's got a transnational goal of a caliphate, because it's radical, because it's got this ludicrously absurd... approach to Islam, they can't help but break that coalition," he said.

"They want a social-religious discipline from the Sunni population in Iraq, who don't want to give it to them."

"They didn't in 2005, 2006," Dodge said, referring to the height of Iraq's Sunni insurgency, "and they don't now."