The families of three Britons killed in a shooting spree in the French Alps said they were "heartbroken" by their deaths but "touched by the expressions of sympathy from people all over the world".
Engineer Saad al-Hilli, his wife and mother-in-law were brutally murdered in a remote spot close to Lake Annecy a week ago.
Ahmed Al-Saffar, the brother of Mrs al-Hilli's dead mother, said: "The victim's family and I are heartbroken by this shocking crime and we have been touched by the expressions of sympathy from people all over the world.
"The victim's family are of Iraqi-Arabic origin. We are very grateful for the support provided by the British, French and Iraqi authorities during this difficult time.
"We hope that those responsible for the deaths of our loved ones are brought swiftly to justice.
"In the meantime, we would ask that the media understand that as a family we need time to grieve and we would therefore request that they respect our privacy at this intensely difficult time."
The statement, on behalf of the al-Hilli and Al-Saffar families, came as Annecy's chief prosecutor Eric Maillaud spoke about the investigation's progress.
Mr Maillaud is due to travel to the UK as part of an investigation into the murder, with examining magistrate Michel Mollin, another senior member of the inquiry team.
They will join a small number of French investigators already in Britain to help unravel the mystery surrounding the deaths of the three Britons and French cyclist Sylvain Mollier, 45, who apparently stumbled across the attack.
Mr Maillaud told reporters that he hoped the inquiry would progress as quickly as possible. He said the scene of the crime had been protected by the gendarmerie again as witness statements were being checked for timings of sightings, which often changed when people thought for longer about what they had seen.