Daish claimed responsibility on Monday for a New Year's Day mass shooting in a packed Istanbul nightclub that killed 39 people, an attack carried out by a lone gunman who remains at large.

The militant group made the claim in a statement on one of its Telegram channels, a method it has used to claim attacks in the past.

There was no immediate comment from Turkish officials.

"In continuation of the blessed operations that Daish is conducting against the protector of the cross, Turkey, a heroic soldier of the caliphate struck one of the most famous nightclubs where the Christians celebrate their apostate holiday," the statement said.

NATO member Turkey is part of the US-led coalition against Daish and launched an incursion into Syria in August to drive the radical Sunni militants from its borders.

The authorities believe the assailant may be from a Central Asian nation and suspect he had links to Daish, Turkey's Hurriyet newspaper said.

Police distributed a hazy black-and-white photo of the alleged attacker taken from security footage.

The shooting at the Reina nightclub on the shores of Istanbul's Bosphorus waterway shook Turkey as it tries to recover from a failed July coup and a series of deadly bombings in cities including Istanbul and the capital Ankara, some blamed on Daish and others claimed by Kurdish militants.

Some people jumped into the Bosphorus to save themselves after the attacker began shooting at random just over an hour into the new year.

Witnesses described diving under tables as he walked around spraying bullets from an automatic rifle.

Nationals of Saudi Arabia, Morocco, Lebanon, Libya, Israel, India, a Turkish-Belgian dual citizen and a Franco-Tunisian woman were among those killed, officials said.

Saudi newspaper al-Riyadh said five of the dead were from Saudi Arabia.

Security services had been on alert across Europe for new year celebrations following an attack on a Christmas market in Berlin that killed 12 people.

Only days ago, an online message from a pro-Daish group called for attacks by "lone wolves" on "celebrations, gatherings and clubs".