The brother of Staff Sgt Denise Rose, the first female UK soldier to die in Iraq, said her family in Liverpool are trying to come to terms with her death.
Staff Sergeant Rose was found dead in Basra on Sunday
Sean Rose said: "We are all too upset to speak about what has happened at the moment."
Staff Sgt Rose, of the Royal Military Police's Special Investigation Branch, was found dead from a gunshot at a Basra military camp on Sunday.
The Ministry of Defence said her death was not from hostile action.
Mr Rose said the family of the 34-year-old, including her mother Florence, were devastated by her death.
"We are asking everyone to respect our privacy at this difficult time," he said.
Since the beginning of the war in March 2003, 31 male British soldiers have died in action - including seven in so-called friendly fire incidents.
A further 31 have died in accidents, two in incidents involving explosive devices, and five from natural causes, illness or unexplained incidents.
Lt Col Robert Silk, commanding officer of her parent unit, the SIB (Germany), based at Rheindahlen, said: "Denise had a multitude of friends, being universally
popular, intelligent and ever cheerful.
"She was doing so well in the Army, and had a
bright future in front of her."
The death was "a terrible shock for all
her many comrades in the unit" and a tragic loss, Col Silk added.
Staff Sgt Rose joined the Royal Military Police in 1989 and trained as a
Special Investigation Branch (SIB) investigator in 1995, conducting
investigations into serious incidents within the military in the UK and Cyprus,
said the MoD.
The statement added: "She deployed as a volunteer to Iraq on 27 September operating as part of a small team of specialist investigators to provide
security for the people of Iraq and assist in the rebuilding of the country
through the provision of a well-trained police force."
A ceremony for those who have died in Iraq will take place on Tuesday afternoon in Trafalgar Square, London.
Mayor Ken Livingstone and Nobel Prize winner Professor Joseph Rotblat are due to attend the "Naming of the Dead" ceremony, which is scheduled to take place simultaneously in several British cities as well as in Baghdad, Sydney and Barcelona.