Daesh jihadists Monday claimed the shooting rampage at a glamorous Istanbul nightclub that killed 39 people on New Year's night, while police arrested eight suspects but the attacker remained on the run.

The statement by the extremist group -- which Turkey is fighting in neighbouring Syria -- was the first undisputed claim it has made for an attack in Turkey despite being blamed for several assaults over the last year.

Anti-terror police made their first arrests over the attack, which unleashed scenes of panic among party-goers at one of Istanbul's swankiest venues and killed mostly foreign tourists.

The shooting took place just 75 minutes into 2017 after a bloody year in Turkey in which hundreds of people were killed in violence blamed on both Daesh and Kurdish militants.

In a statement circulated on social media, the jihadist group said one of the "soldiers of the caliphate" had carried out the attack on the Reina nightclub.

It accused Turkey, a majority-Muslim country, of being a servant of Christians, in a possible reference to Ankara's alliance with the international coalition fighting Daesh in neighboring Syria and Iraq.

Arriving by taxi at the plush Reina nightclub on the shores of the Bosphorus, the gunman produced a weapon, reportedly a Kalashnikov, and shot dead a policeman and civilian at the entrance.

He then fired off four magazines containing a total of 120 bullets around the club which was filled with an estimated 700 people.

But after changing clothes, the gunman left the nightclub in the ensuing chaos and has managed to evade security forces.

There were no reports that security services had come close to detaining the gunman but physical and fingerprint data had been obtained.

Hurriyet daily said investigators believe the gunman may be from the Central Asian states of Kyrgyzstan or Uzbekistan.