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

"In continuation of the blessed operations that Islamic State 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 Islamic State and launched an incursion into Syria in August to drive the radical Sunni militants from its borders.

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

Police have 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.

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.

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

- AAP