The attack on one of the world's busiest airports, a hub at the crossroads of Europe and Asia, was the deadliest in a series of suicide bombings in Turkey this year.
The official gave no further details beyond confirming the attackers' nationalities and declined to be named because details of the investigation have not yet been released. Forensics teams had been struggling to identify the bombers from their limited remains, officials said earlier.
Interior Minister Efkan Ala told parliament that evidence continued to point to Islamic State responsibility and that the death toll had risen to 43, of whom 19 were foreigners. Ala said the identity and nationality of one of the bombers had been determined but did not comment further.
The pro-government Yeni Safak newspaper said the Russian bomber was from Dagestan, which borders Chechnya, where Moscow has led two wars against separatists and religious militants since the Soviet Union collapsed in 1991.
Turkey's Hurriyet newspaper named him as Osman Vadinov and said he had come from Raqqa, the heart of Islamic State-controlled territory in Syria. The Russian interior ministry said it was checking information about Vadinov.
A spokesman for Kyrgyzstan’s state security service said it was investigating, while the Uzbek security service had no immediate comment.
The revelation that one of the attackers was a Russian national comes at an awkward time for relations between Ankara and Moscow, strained since Turkey shot down a Russian warplane near the Syrian border last November.