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.
"The scene of the crime has been cordoned off again today. We will return to the scene of the crime in the coming days," he told journalists.
Mr Maillaud is due to travel to the UK on Thursday 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.
French media has recently speculated about the "unanswered questions" from the police investigation into the shooting massacre of three members of a British family and a French cyclist.
Local paper Le Dauphine raised four key questions about the crime scene, after the area was reopened this week.
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.
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Crime coordinator Capt. Laurent Dourel, left, Annecy prosecutor Eric Maillaud, second left, and French Gendarmes Col. Bertrand Francois, third left, and Lt. Col. Benoit Vinneman atttend a news conference in Annecy, French Alps, on Thursday, Sept. 6, 2012. (AP Photo/Lionel Cironneau)
Annecy prosecutor Eric Maillaud answers a question during a news conference in Annecy, France, on Thursday, Sept. 6, 2012. (AP Photo/Lionel Cironneau)
A gendarme blocks access to the site where people were shot to death near Chevaline, French Alps, on Thursday, Sept. 6, 2012. (AP Photo/Laurent Cipriani)
A Gendarme's car heads to a killing site near Chevaline, the French Alps, on Wednesday, Sept.5, 2012. (AP Photo/Alexis Moro)
Gendarmerie Col. François, left, and Annecy prosecutor Eric Maillaud answer reporter near a killing site, near Chevaline, the French Alps, on Wednesday, Sept. 5, 2012. (AP Photo/Alexis Moro)
Gendarmes block access to a killing site near Chevaline, the French Alps, on Wednesday, Sept. 5, 2012. (AP Photo/Alexis Moro)
Gendarmes blocks access to site where people were shot to death near Chevaline, the French Alps, on Thursday, Sept. 6, 2012. (AP Photo/Laurent Cipriani)