Police released pictures of the suspect who went on the rampage at the plush Reina nightclub on New Year's night, spraying some 120 bullets at terrified guests before slipping away into the night.
So far, 16 people are being held over the attack, including two foreigners detained by Turkish police at Istanbul's main airport. But the killer remains on the run.
Of the 39 dead, 27 were foreigners, mainly from Arab countries, with coffins repatriated overnight to countries including Lebanon and Saudi Arabia.
The suspect -- who has not been named but was reportedly from Central Asia -- was staying in a rented flat in Konya before moving to Istanbul to carry out the attack, press reports said.
The Dogan news agency said those detained included a woman suspected of being his wife with whom he had stayed in Konya along with two children.
Reports said police have made progress in the investigation after speaking to the taxi driver who drove the attacker to the club and tracing calls he had made on the driver's mobile phone.
Hurriyet's well-connected columnist Abdulkadir Selvi he had been trained in street fighting in residential areas in Syria and used these techniques in the attack, shooting from the hip rather than as a sniper.
The attacker had been "specially selected" to carry out the shooting, he said. According to Hurriyet, just 28 bullets failed to hit a target.
"This specially-trained terrorist has still not been detained and is still wandering dangerously amongst us," he wrote.
He said an IS strike was also planned in Ankara on New Year's eve but that it had been prevented after eight IS suspects were arrested in the capital. There were no further details.
Police meanwhile released the first clear images of the attacker, including one taken by security cameras on the night of the attack.
And a chilling video of the suspect taken near Taksim Square in central Istanbul was also released, showing him recording himself with a selfie stick and smiling faintly into the camera.
It was not immediately clear how the footage had been obtained.
Reports said that the attacker could be from Kyrgyzstan or Uzbekistan. In Bishkek, the national security council said it was checking any possible involvement of a Kyrgyz citizen.
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