The US military reported two raids in Sadr City, one of which netted two members of a kidnap gang and the other a six-strong "terrorist cell" accused of smuggling guns, shells and roadside bombs from Iran.
Sadr City residents said two of those arrested on Wednesday were Iraqi police, but the military could not confirm the raids were linked to the missing Britons.
Hoshyar Zebari, the foreign minister, said: "We are pursuing this case very vigorously, I would say, because the nature of this kidnapping is very strange.
"The location of this finance ministry computer centre and the nature of the operation and the number of people involved, I think all indicate more a militia than a terrorist group, let's say."
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In an interview with BBC radio, Zebari noted the raid had taken place near Sadr City, a stronghold for al-Mahdi army of Muqtada al-Sadr, the Shia leader, but he said it was too soon to blame a specific group.
Zebari said the nature of the kidnapping clearly pointed to the involvement of one of the Shia groups that have infiltrated Iraqi forces, rather than to a Sunni outfit such as a-Qaeda in Iraq.
The Kurdish cabinet member's comments came on a day US forces handed over responsibility for security in Iraq's three northern provinces to the Kurdish regional government at a ceremony in Irbil.
Officials said the autonomous region will work closely with the national government in Baghdad.
Representatives of al-Sadr's movement, which fields thousands of militia fighters, categorically denied any involvement in Tuesday's abductions.
The Iraqi presidency, prime minister's office and interior ministry refused to comment.
Four of the five Britons were members of a security detail working for Garda World, a Canadian firm, while the fifth was their client, a consultant under contract to the US government to train Iraqi civil servants.
Witnesses to the abduction said it unfolded without much violence after four blue and white pickup trucks with crude armour welded on them, like those used by the national police, pulled up to the building.
Three journalists have been shot dead over the past three days in Iraq, according to their colleagues.
On Wednesday, armed men killed Nezar Abdul Wahid al-Radi in the southern city of Amara as he prepared for a journalism workshop with colleagues.
|A policeman in Kirkuk being treated by doctors|
after an attack by Sunni fighters [EPA]
In the mainly Sunni city of Falluja, 50km west of Baghdad, Abdel Rahman al-Issawi, a journalism professor, was murdered by armed men together with six of his family members on Monday night, according to witnesses quoted by the independent daily al-Mada.
In the northern city of Kirkuk, armed men shot dead Mahmud Hassib al-Qassab, the editor in chief of the weekly al-Hawadith and the head of the Turkmen Salvation Movement, in the Turkmen district of Musala.
On Wednesday, several mortar rounds apparently targeting a US military base in Falluja missed their mark and landed instead in a court house and in a residential neighbourhood, killing nine civilians and wounding 15 others, according to police and medical sources.A woman was killed and two policemen injured during clashes between fighters and policemen in Mosul, 390km north of Baghdad.
A police commander's convoy was struck by a roadside bomb in the town of Hamza, south of Baghdad, killing two guards and injuring two others, a police officer said.
And two Iraqi soldiers were killed and two others wounded in an explosion in Diwaniya.
Iraqi police found 30 dead bodies in different areas in Baghdad on Tuesdsay.