A defence ministry spokeswoman told AFP that the arrests followed the latest allegation of deliberate abuse.
She did give details of where and when the latest arrests occurred, or even whether the two men were soldiers.
Corporal Martin Webster of the 1st Battalion Light Infantry was the first person arrested over the scandal.
It remains unclear whether he is being held as a witness or perpetrator.
The BBC has broadcast a 2004 interview with Corporal Webster in which he talked about filming events during his tour of duty.
He described how locals were "really, really accepting" at first but "the last month was absolutely hell."
The ministry has confirmed that the 1st Battalion Light Infantry,
from Paderborn, Germany, was assisting the investigation.
The Battalion served in Iraq from the March 2003 invasion until April 2004.
The ministry's investigation came after the News of the World broke the story on Sunday and published stills from the video.
In the fuzzy video, troops appear dragging four young Iraqi civilians off a street and into an army compound.
The youths are seen being punched, kicked and hit with batons.
The video is thought to have been filmed in 2004 during street
riots in southern Iraq, where British forces are concentrated.
The News of the World said the scenes were filmed by a corporal
who can be heard encouraging his colleagues.
It has since been aired on television worldwide.
A government spokesman described the allegations as “extremely serious” but said the investigation was at an early stage.
More evidence must be gathered before a decision could be made on whether the soldier will face a court martial.
Compensation
Iraqi officials have called for an immediate inquiry.
National security adviser Mowaffaq al-Rubbaie said if the allegations were true, it was not acceptable.
He stressed that soldiers found guilty “must compensate the victims and apologise to them directly.”
Safety fears
All British units in Iraq have reportedly been put on alert because of concerns the pictures could provoke a Muslim backlash.
Since the 2003 US led invasion of Iraq to oust Iraqi President Saddam Hussein, Britain has deployed 80,000 troops there.
The troops’ priority now is to work to restore security and build democracy in Iraq.
Analysts have warned that the footage could bolster a feeling among Muslims that they are vulnerable to abuse.
There are fears that it could fuel rage demonstrated by the reaction to caricatures of the Prophet Mohammed in European newspapers.
Britain has until now avoided much of the fallout as most news organisations have largely refrained from carrying the caricatures.