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 victims' 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 victims' 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 tomorrow 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 today as witness statements were being checked for timings of sightings, which often changed when people thought for longer about what they had seen.
As for the al-Hillis' seven-year-old daughter Zainab, who survived the killings, Mr Maillaud said: "She will, of course, be listened to very specifically, but her doctors have got to be able to help her try to get back to the best possible health, and eventually hope she will express herself."
He said she is a key witness - "the only person alive who actually could have seen something" - but warned that she is seven years old and has been "very damaged".
Mr Maillaud said 40 French officers were working on the complex case which has led to a flurry of theories relating to possible motives.
But he gave no indication that French authorities were any closer to solving the murders, suggesting it could be years before answers emerge.
Investigators are focusing on three specific areas - Mr al-Hilli's work, his family and his native Iraq.
The latter has been at the centre of considerable attention and Mr Maillaud said a "specialised" team was tasked with examining Mr al-Hilli's links to the country.
He said: "The fact that he was born in Iraq, that he had family in Iraq, of course that's something that is of interest and we are asking ourselves if there is a link between that and his death.
He added: "There are specialised people as far as Iraq is concerned who are looking at it, in other words, people who know who to contact in order to be able to work with that country so, for example, we have a security attache we are working with."
Mr Maillaud said the large part of the investigation was taking place in the UK and that French authorities believe there could be a "great number of clues" in Britain.
But he refused to be drawn on the main area of the inquiry's focus.
Mr Maillaud said investigators had no plans to travel to Sweden, where Mrs al-Hilli's mother, named in reports as Suhaila al-Allaf, 74, was living.
But he said police would interview a relative in Sweden, if it transpired that reports relating to his alleged history of violence proved to be correct.
In Annecy, numerous witnesses have already come forward, he said.
They include a hiker, named only as Philippe D, 41, who likened the carnage to a horrific film scene.
The walker described arriving at the site of the massacre, in the Combe d'Ire forest, near Chevaline, minutes after the attack at around 4pm last Wednesday.
There, in a small car park, he found the bodies of Mr al-Hilli, 50, his dentist wife Iqbal, 47 and Mrs al-Allaf in their bullet-ridden BMW.
A fourth body, that of Mr Mollier, lay nearby.
The al-Hilli's daughter Zainab, seven, was lying by the car. She had been brutally beaten and shot in the shoulder and is now recovering from her ordeal in hospital.
Her sister Zeena, four, escaped unscathed by cowering behind her mother as bullets rained down. She has flown back to Britain with carers.
Sources said the victims were likely to have been blasted with the same gun, fuelling speculation they were targeted by a contract killer. Each person was shot twice in the head.
Detailed ballistic analysis of 25 spent cartridges found at the scene suggests they all came from a 7.65mm automatic pistol.
The gun has been described as an old-fashioned weapon but one that can still be used by special forces.
Officers are now examining all aspects of Mr al-Hilli's life to find a motive for the murders.
Mr Maillaud will visit the al-Hilli family home in Claygate, Surrey, tomorrow afternoon as part of a 24-hour trip to the UK.
Yesterday officers were examining a safe at the mock Tudor house which has been the subject of intense police searches for five days.