An independent ombudsman should lead inquiries into the deaths of Iraqi civilians allegedly killed by coalition forces, an MP has said.
UK troops had to intervene during a demonstration in Basra on Tuesday
Adam Price of Plaid Cymru wants an "impartial" non military investigation.
His call comes after the MoD said it had paid £8,125 in compensation to the families of three Iraqi civilians allegedly killed by UK troops.
Armed Forces Minister Adam Ingram said the current complaints procedure was sufficiently independent and robust.
As well as the three deaths for which compensation had been paid, the MoD was also investigating claims over the deaths of 13 other Iraqi civilians since 1 May, a spokesman said.
The payouts were not an admission of guilt, he stressed, adding that all the deaths were still being investigated by the Royal Military Police (RMP).
But Mr Price said it was "simply not acceptable for the military to be investigating themselves and deciding on an ad hoc basis whether or not to award ex gratia payments to the families of the deceased".
In a Commons debate on Wednesday, he called for an independent investigation into all allegations of civilian deaths involving coalition forces.
This could involve "possibly the appointment of an independent ombudsman in the
coalition [provisional] authority that could oversee all complaints," he said.
Mr Price's call was backed by human rights group Amnesty International UK, which said it was "imperative" that all investigations into alleged civilian deaths at the hands of UK troops were "civilian-led and supervised".
"Receiving compensation does not mean that justice has been done and been seen to be done," said spokeswoman Lesley Warner.
"All investigations must be prompt, impartial and independent and seen to be so. It is not enough for the army to investigate the army."
But Mr Ingram defended the way in which the RMP carried out its investigations.
He said serious cases could be referred to the Army Prosecuting Authority, which was independent of the chain of command and answerable to the Attorney General
"We regard any loss of civilian life as deeply regrettable, and we take our obligations to avoid, or else minimise, civilian casualties extremely
seriously," he said.
"Steps to avoid such casualties are integrated into every aspect of military operations.
"Where there is any indication that these measures may have failed, we investigate fully, in order to learn the lessons that will make incidents of
civilian death and injury fewer still."
The MoD has paid £6,625 to 19 Iraqi civilians allegedly injured in incidents involving British troops.
A spokesman said 39 further allegations of injury were still being investigated.