The plane crashed in Syria after violating Turkey's airspace, the country claims
It was just over the Syrian border when it was downed by F16 Fighting Falcon jets belonging to Turkey, the official added
But the Russian Defence Ministry said the plane had not violated Turkey's airspace and was flying at an altitude of 6,000 metres.
NATO has announced it will be holding an extraordinary session at 4.30pm GMT after Turkey requested it following the incident.
Russian President Vladimir Putin has called an emergency meeting in Russia over the downing of the jet and unverified sources have claimed Russia is currently sending a warship across the Dardenelles from the Black Sea into the Mediterranean.
The jet is reported to be a Russian Su-24 flown by a pair of Russian pilots, with one believed to have been captured by Syrian rebels from the Alweya Al-Ashar (Brigade of the 10th) which consists of Turkmen with strong links to Turkey.
Russia is currently fighting in Syria with President Bashar al-Assad's troops against the rebels and Islamic State (ISIS).
Sources say the brigade has now launched "a counter-offensive" against President Bashar and Russian troops in a bid to take back the Turkman mountains.
Turkish presidential sources have said the jet was downed in line with the rules of engagement after violating the country's airspace and failing to heed warnings.
He said the pilot was warned 10 times before they deployed the F16s to shoot it down.
A government official said: "We are trying to identify the nationality of the plane."
Russia's foreign minister Sergy Lavrov was expected to land in Istanbul at 4.30pm today - the same time as the urgent NATO meeting - ahead of talks with the Turkish government tomorrow, but so far there is no indication he will be leaving Moscow soon as he is in meetings with Mr Putin.
A statement said: "It would be wrong to talk about consequences and relations between Russia and Turkey at the moment."
Video footage shows a plane exploding in the air before the fireball fell onto a Turkmen mountain near a village on the northern Syrian side of the border.
British foreign secretary, Philip Hammond, said: "Clearly this is a serious incident but it wouldn't be wise to comment further until we have the facts."
The fate of the crew was unknown, the Observatory said, adding that there had been aerial bombardment in the area earlier, where pro-government forces have been battling insurgents on the ground.
Ankara has traditionally expressed solidarity with Syrian Turkmens, who are Syrians of Turkish descent.
About 1,700 people have fled the mountainous Syrian area to the Turkish border as a result of fighting in the last three days, a Turkish official said on Monday.
Russian jets have bombed the area in support of ground operations by Syrian government forces.
He instructed them to consult with NATO and the UN on the latest developments on the Syrian border.
In October, when Russian planes flew into Turkish airspace two days in a row, NATO - of which Turkey is a leading member - released a statement which said: "Allies strongly protest these violations of Turkish sovereign airspace, and condemn these incursions into and violations of NATO airspace. Allies also note the extreme danger of such irresponsible behaviour.
"They call on the Russian Federation to cease and desist, and immediately explain these violations.
"Allies call on the Russian side to take all necessary measures to ensure that such violations do not take place in the future."
The Sukhoi SU-24 is a supersonic, all weather attack aircraft developed in Russia. The aircraft features avariable-sweep wing, twin-engines and a side-by-side seating arrangement for its two crew.
It was the first of Russia's aircraft to carry an integrated digital navigation and attack system.