Eric Maillaud, the prosecutor leading the investigation, said two months after the killings, "all lines of inquiry remain open," the BBC reported Saturday.
Sixty officers have interviewed 800 witnesses in the deaths of Saad al-Hilli, his wife Iqbal and her mother, Suhaila al-Allaf, in the Annecy region of the French Alps, Maillaud said. A fourth victim, a French cyclist, apparently was killed when he was run over by a car al-Hilli was driving in an attempt to get away from the shooter.
The investigation has spanned seven countries and required viewing thousands of hours of film and images from toll booths and roadside cameras.
The suspect is believed to be someone who has killed before, the prosecutor said, a mentally unbalanced person "capable of extreme violence."
Because police have not been able to determine a motive, they are considering the possibility the deaths may have been the result of a random act.
Police said they believe the shooter emerged from the forest trail above the family while al-Hilli and a daughter were outside their car. al-Hilli raced for the car, putting it in reverse and making a U-turn, possibly running over the cyclist. The car then slammed into the bank at the rear of the pull-off and became stuck.
The shooter then killed the adults inside the car.