Andrey Karlov was shot dead by an off-duty policeman in Ankara
Russian and Turkish foreign ministers will meet to discuss the situation in Syria later, a day on from the murder of Moscow's ambassador to Turkey.
Andrey Karlov was killed by an off-duty policeman, who shouted "don't forget Aleppo" after shooting the diplomat.
The 62-year-old ambassador had been attending an art exhibition at the Contemporary Arts Centre in the Cankaya area of Ankara, along with other dignitaries and media.
The gunman was Mevlut Mert Altintas, a 22-year-old who had been working for the riot police squad in Ankara for the past two-and-a-half years.
Russian Foreign Minister Sergey Lavrov said: "We are sure that those who staged that barbaric crime were seeking to derail the process of normalising Russia-Turkey ties primarily with a goal to prevent an efficient fight against terrorism in Syria.
"This attempt is futile."
An Taoiseach Enda Kenny said: "I condemn the callous murder of Russia's Ambassador to Turkey and offer condolences to Ambassador Karlov's family.
"These acts of violence have no place in society and constitute an attack on our fundamental values."
Meanwhile, US Secretary of State John Kerry called the assassination a "despicable attack" and President-elect Donald Trump said it was a "violation of all rules of civilised order" and said it must be "universally condemned".
On Monday night the United Nations Security Council condemned "in the strongest terms" the assassination of Mr Karlov, and called for the perpetrators, organisers and sponsors to be brought to justice.
Altintas was off-duty when it is understood he entered the building using his police ID and opened fire on the ambassador as he made a speech.
A video showed him shouting: "Don't forget Aleppo, don't forget Syria!
"So long as our brothers are not in safety, you will not taste safety either. Only my dead body will leave here.
"Whoever is involved in this cruelty, one by one, you will pay for it."
The gunman also shot three other people, although none were seriously injured, according to Turkey's interior ministry.
He then climbed to the second floor of the building before a 15-minute shootout with police, during which he was killed.