With the Turkish capital already on high alert after a string of attacks this year, an individual also fired outside the US embassy in Ankara overnight in a separate incident.
President Vladimir Putin declared "we have to know who directed the hand of the killer" and the Kremlin said a Russian investigative team were flying to Turkey to probe the murder.
An unprecedented three-way meeting between the foreign ministers of Turkey, Russia and Iran in Moscow over the Syria crisis was meanwhile set to go ahead despite the killing.
Dramatic images showed Karlov stumble and then crash to the ground on his back as the attacker brandished his gun at terrified onlookers who cowered behind cocktail tables.
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The gunman shouted and then said all those responsible for what has happened in Syria and Aleppo would be held accountable.
Altintas had set off the metal detector security check when he entered the exhibition in central Ankara as he was carrying a gun, the pro-government Sabah daily said.
The Hurriyet daily added that Altintas, who had worked for Ankara's anti-riot police for the last two and a half years, had stayed at a nearby hotel to prepare for the attack.
It said Altintas, who was off duty at the time, had put on a suit and tie and shaved at the hotel before heading to the exhibition centre.
He was later killed by police after a shootout that lasted over 15 minutes.
Altintas was born in the town of Soke in Aydin province in western Turkey and attended a special school for training future policemen.
The mayor of Ankara, Melih Gokcek, known for his outspoken comments, speculated on his official Twitter account that the attacker may be linked to the group of Fethullah Gulen, blamed for the July 15 coup aimed at toppling President Recep Tayyip Erdogan.
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