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.
More top news
Team Sky's Chris Froome is set to win the 2016 Tour de France with an overall lead of four minutes 11 seconds after stage 20 to Morzine
The attempted kidnap of an RAF serviceman took place near RAF Marham, in Norfolk, on Wednesday.
Footballer Marc Crosas faces an investigation after pictures emerged of him appearing to have speared an endangered baby shark