In an opening statement today, counsel to the inquiry Jonathan Acton Davis QC said it aims to identify the circumstances of the deaths of 28 Iraqi men.
The claim related to events which began on May 14 2004, when Iraqi insurgents ambushed vehicles belonging to the Argyll and Southern Highlanders near to a permanent vehicle checkpoint known as Danny Boy which was some 5km north-east of Majar Al Kabir on route six in Iraq.
A fierce battle ensued which involved not only the Argylls but also soldiers from the Princess of Wales Royal Regiment.
It resulted in many Iraqis being killed and in two British soldiers being wounded.
He said enemy dead would normally have been left on the battlefield, but British soldiers were apparently given an order to identify the dead to try to find a man thought to be involved in the murder of six British soldiers in 2003.
As part of that order, the bodies of 20 Iraqis were taken back to CAN, and nine were detained, he said.
It was the claimants' case that not all of the 20 died on the battlefield, and that at least one of them was murdered by a British soldier after he had been returned alive to CAN.
A long-awaited public inquiry into claims that British soldiers mistreated and murdered Iraqi detainees during the Iraq War has opened.
The Al-Sweady Inquiry is examining claims that UK soldiers murdered and tortured Iraqis after the "Battle of Danny Boy" in Maysan Province, southern Iraq, in May 2004.
It will look at allegations that Iraqis were unlawfully killed at Camp Abu Naji (CAN) on May 14 and 15 2004 and that five Iraqi detainees were tortured and ill-treated at CAN, and again between May 14 and September 23 2004, at a detention facility at Shaibah Logistics Base.
Patrick Mercer, Conservative MP for Newark, said he "did not expect very much at all" to come out of a long-awaited inquiry into claims that British troops murdered and tortured civilians during the Iraq War.