The latest clashes, just weeks before parliamentary elections, raise key questions over the capacity of the army and police to repel militant attacks.
Anti-government fighters currently hold all of Fallujah, a town that is just a short drive from Baghdad, and other pockets of territory.
The push by the Islamic State of Iraq and the Levant (ISIL) into the Abu Ghraib area, sparking clashes in nearby Zoba and Zaidan, as well as a failed assault on a military camp in Yusifiyah, illustrate the group's ambition, even with Fallujah under military siege.
In perhaps the most worrying sign of ISIL's capabilities, anti-government fighters paraded with dozens of vehicles last week in broad daylight in Abu Ghraib, just 20 kilometres (12 miles) from the capital, according to witnesses and videos posted to YouTube.
"ISIL fighters are trying to ease the pressure imposed on them in Fallujah," said an army lieutenant colonel, speaking on condition of anonymity.
"They have begun moving against weak villages between Baghdad and Fallujah, and to attack army units."
A police colonel, who also declined to be identified, added: "Members of ISIL have begun launching attacks on the army deployed in Abu Ghraib, and are threatening Baghdad."
In early January, militants overran Fallujah and parts of Ramadi, two towns in the western desert province of Anbar which shares a long border with Syria.
Government security forces have wrested back control of much of Ramadi.
But a stalemate has persisted in Fallujah, with periodic clashes on the city's outskirts and regular shelling of what the army says are militant strongholds.
But for around a week, soldiers have fought fierce battles in Zoba and Zaidan, which lie between the capital and Fallujah.
At least three people have been killed and more than 50 others wounded in the clashes and army shelling, according to medical sources.
"The objective appears to be to use this Anbar base as a launching pad for expansive operations towards the federal government in Baghdad," said Charles Lister, a visiting fellow at the Brookings Doha Center.
Lister said the massive convoy in Abu Ghraib, in particular, "underlines the sheer scale of (ISIL's) capacity to operate with near impunity in some Sunni areas of the country."
"Iraqi security forces face some serious challenges to confronting (ISIL's) continued expansion in Iraq."
Senior security officials insist, however, that any move towards Baghdad by the jihadists is doomed to failure, and that attempts to open a new battlefront are a sign of weakness rather than strength.
"Entering Baghdad is impossible, this is not logical," said Brigadier General Saad Maan, spokesman for the interior ministry and the Iraqi capital's security command centre.
"They do not have the power, and we have huge military reinforcements to stop them. Our military has launched attacks against them on a daily basis in the Fallujah suburbs, and they have suffered lots of casualties."
- ISIL 'dreaming' -
Another senior security official, who spoke on condition of anonymity, said ISIL fighters were "dreaming" if they thought they could break through.
"The siege of Fallujah will continue until their gathered forces are depleted," the official said. "Fallujah is the last stronghold of ISIL in Anbar."
The latest battles are part of a protracted surge in bloodshed that has pushed violence to its highest level since 2008, when Iraq was emerging from a brutal Sunni-Shiite sectarian war that left tens of thousands dead.
The unrest has been driven principally by anger in the Sunni Arab minority over alleged mistreatment at the hands of the Shiite-led government and security forces, as well as spillover from the war in Syria.
Diplomats and analysts have urged the authorities to reach out to the Sunni community to undermine support for militancy.
But with parliamentary elections looming at the end of this month, Prime Minister Nuri al-Maliki and other Shiite leaders have been loath to be seen to compromise.