By Crispin Thorold
BBC News, Baghdad
Significant numbers of UK and US troops are supporting the Iraqi military
From the beginning, the US government has characterised the operations against Shia militias in Basra and Baghdad as an Iraqi-led and executed campaign.
It is now clear that although the initial military planning was Iraqi, US and British forces are deeply involved.
In the capital's neighbourhood of Sadr City, US infantry troops are fighting alongside Iraqi soldiers, to try to secure areas that were once firmly under the hold of the Mehdi Army, which is loyal to the Shia cleric, Moqtada Sadr.
Reports suggest that US combat units have also been deployed at short notice to Basra from elsewhere in Iraq and the Middle East.
On Monday, a US convoy in the southern city was attacked. A spokesman for the US-led coalition confirmed the bombing, but would give no further details.
A Western military source has also told the BBC that significant numbers of UK and US special forces are in Basra, acting both independently and in support of Iraqi army units.
Much of the work that the Western special forces are doing is "mentoring and encouraging" their Iraqi counterparts, the source said.
However, it is believed that they are also carrying out operations to detain "high-value individuals" from the Mehdi Army, other militias and local tribes.
According to the source, the special forces personnel are also gathering intelligence to support ground operations.
'Considerable work needed'
The growing involvement of the US-led coalition in the fighting may be a tacit acceptance that the Iraqi security forces are not yet up to the job.
In his recent testimony to the US Congress, the top US military commander in Iraq, Gen David Petraeus, said there were now 540,000 Iraqi policemen and soldiers serving but he raised doubts about their capabilities.
More than 1,300 soldiers and police have been dismissed for desertion
"While improved, Iraqi security forces are not yet ready to defend Iraq or maintain security throughout the country on their own", he said.
"Recent operations in Basra highlight improvements in the ability of the Iraqi security forces to deploy substantial numbers of units, supplies, and replacements on very short notice," he added.
"On the other hand, the recent operations also underscored the considerable work still to be done in the areas of logistics, force enablers, staff development, and command and control."
There were also many desertions from the Iraqi security forces. About 1,000 personnel - including a full infantry battalion - refused to fight or joined the militias during last month's offensive.
More than 900 police and soldiers have been sacked in Basra, including nearly 40 senior police officers, where the fiercest clashes took place. A further 400 police officers were dismissed in Kut.
On Iraqi deserter interviewed by the BBC, who does not want to be named, said there were chaotic scenes in the early days of the fighting in Basra.
"Half of our officers were hiding. The lower rank soldiers had to fight in the streets", he said.
"For four days we didn't have anything to eat - it was chaos. We didn't have any senior officers to tell us what to do. We were left alone."
A senior Iraqi officer described the deserter as a traitor.
"It's a matter of public record that all the senior officers were on the frontline, and with such an example it's inconceivable that junior officers would have been in hiding", the officer said.
During the most intense fighting in Basra and Baghdad, scores of soldiers were filmed handing their weapons over to clerics at the offices of Moqtada Sadr.
Those images were dismissed as publicity stunts at the time, but it is clear that several soldiers chose not to fight.
Their reasons vary - some may have been the radical cleric's supporters all along, the families of some serving soldiers were reportedly threatened by the Mehdi Army, and others simply did not want to kill their countrymen.
The Iraqi government has blamed the militias for any civilian casualties
"I don't want to fight Iraqis. I don't want to fight Muslims", said the deserter we interviewed. "How can someone fight his brother or his cousin? How can that be possible?"
"The soldiers shot at houses and destroyed them completely. Young men, women and children got killed", he added.
Those claims have been dismissed by the Iraqi ministry of defence, which claims that it was only the militias that killed civilians.
"Not one was killed by the army - the army used no mortars or artillery shells, only light weapons to limit danger to civilians", said a senior Iraqi officer.
Whatever the truth of the claims and counter-claims it is clear that there are still serious doubts about the capability of the Iraqi security forces.
US policy in Iraq is dependent of its soldiers and policemen. Eventually the US wants to hand over responsibility for the country's security to them.
For now, though, it appears that coalition forces will continue to have a significant role against Shia militiamen.