"In light of the facts and the killer's explanations, there does not seem to be any link between the two cases," Annecy prosecutor Eric Maillaud told AFP.

"Exchanges have taken place, but there is now no reason to go further," he said.

French investigators had asked police in Switzerland for permission to question the gunman, who went on a shooting spree last Wednesday in the Swiss village of Daillon.

Police in France have been struggling to solve the case of the shootings last year in the Haute-Savoie department, where Saad al-Hilli, his wife Iqbal and her mother Suhaila al-Allaf were all found dead inside their estate car near Lake Annecy on September 5, along with a French cyclist who investigators believe was an innocent bystander.

The couple's two young daughters survived the attack, which took place in the village of Chevaline, about 150 kilometres (90 miles) from Daillon.