PARIS - French prosecutors have formally opened an investigation into the robbery in Paris of Kim Kardashian in which the United States reality TV star lost millions in jewellery, a judicial source said on Wednesday (Oct 12).

The investigation is focusing on "armed theft in a gang, criminal conspiracy and kidnapping", the source said.

DNA traces that were found in the luxury apartment where Kardashian and her entourage were staying are being examined, another source told AFP.

Police said a gang of five armed men burst into the residence in the early hours of Oct 3, tied up Kardashian and stole a ring and jewellery worth around nine million euros (S$13.7 million).

They are believed to have fled the scene by bicycle.

Kardashian, 35, who had been attending Paris Fashion Week, was briefly questioned by police before flying back to New York.

The star's bodyguard, Pascal Duvier, was not with her at the time of the attack because he was providing security for Kardashian's sister Kourtney at a Paris nightclub.

Kardashian, who is married to rap star Kanye West, has kept a low profile since returning home.