By Jim Muir
BBC correspondent, Baghdad
Five Britons were taken from Baghdad's finance ministry
Although both have many other preoccupations on their minds, both the Multinational Forces and the Iraqi government are taking the abduction of five British citizens from a Finance Ministry building in Baghdad on Tuesday very seriously indeed.
A special joint emergency room has been set up.
On the basis of leads and information it receives, US and Iraqi government troops have been raiding "targets" - apparently often ordinary homes - in Sadr City, the densely populated mainly Shia suburb on the east side of Baghdad where the Mehdi Army militia has a major presence.
At the same time, political contacts are under way through Iraqi government and religious channels to try to establish who is holding the five men and negotiate their release.
Fears have been expressed that heavy-handed raids on the ground - which have apparently yielded little so far - may upset the political efforts to get the Britons back safe and sound.
The fact that the raids have been concentrated on Sadr City underlines the apparently prevailing working assumption that the five men - a computer expert and his four bodyguards - were abducted by Shia militants from the Mehdi Army.
From the outset, officials and spokesmen for the movement in Baghdad, Najaf and Basra have vehemently denied any connection with the kidnapping.
Yet the suspicion has stuck.
Whether or not it is bolstered by credible intelligence information, there is a mass of circumstantial evidence pointing in that direction and few other serious contenders in the frame.
The Mehdi Army is believed to have lost much of its cohesion, and to involve a number of splinter groups.
The extent to which its acclaimed leader, the radical young Shia cleric Moqtada Sadr, has a grip over the whole organisation is in serious doubt.
The abduction was clearly a large, meticulously planned and coolly executed operation involving major logistical and intelligence capabilities.
It could not have been the work of some minor ad hoc grouping.
The Mehdi Army has been blamed for a number of similarly audacious daytime raids in the past, involving either rogue police and army units or gunmen masquerading as such, and carrying out mass abductions of Iraqis.
So apparently it has the experience and expertise.
The Finance Ministry building which was raided is close to the Mehdi Army's stronghold in Sadr City.
Iraqi sources say the militia's influence throughout that area is strong. It's been virtually ruled out that Sunni insurgent groups would dare operate so flagrantly in such a district.
The other major Shia militia, the Badr Organisation, is part of the Supreme Council for the Islamic Revolution of Iraq (SCIRI).
Moqtada Sadr's control over the Mehdi Army is in doubt
One of its most prominent members, Bayan Baqer al-Zubaidi, is Finance Minister.
In Iraqi culture, it would be almost unthinkable - but clearly not impossible - that a militia would commit such an act on the premises of its own minister.
At a news conference in Baghdad, Mr al-Zubaidi condemned the abduction and called on "all political and popular forces" to help secure the release of the Britons.
SCIRI has no track record in seizing foreigners, and no particular bone of contention with the British.
But elements of the Mehdi Army are locked in a violent struggle with British forces in the south of the country, where one of its leaders, Abu Qadir, was killed last week during an operation by Iraqi government and British forces.
So it has the motivation.
The British Embassy in Baghdad has warned that further kidnap attempts may be staged, and told UK nationals operating outside the heavily guarded Green Zone to exercise extra caution.
While the Foreign Office in London has said it has reached no conclusion about who staged the abduction, the consular warning seemed to imply a belief that Mehdi Army retaliation was suspected.
The kidnapping has caused embassies based in the Green Zone to suspend operations involving excursions beyond their confines, especially to government ministries lying outside the zone.
The impact on the fledgling Iraqi administration, heavily reliant on foreign expertise, may be considerable.
The experts helping the Finance Ministry had been engaged there for the past four years, trying to construct a nationwide computer network linking ministries and provinces throughout the country.
Previous abductions of Britons attributed to the Mehdi Army have been resolved fairly swiftly and peacefully. But things have changed since then.
For one thing, the violent engagements with British forces in the south have created a bitterness that was not there before.
Mehdi Army militants are also being hunted down in Baghdad under the current security clampdown or "surge" which has driven them off the streets.
The Sadrist movement to which the Mehdi Army belongs also pulled out of the coalition Iraqi government earlier this year, perhaps making it less responsive to political pressures.
Yet it retains some 30 members in the current Iraqi parliament, and it is electorally allied to the Prime Minister, Nouri al-Maleki, and his Daawa Party.
So there are plenty of channels of communication if the Britons really are in Mehdi Army hands.