The Foreign Ministry said the Russian SU-34 fighter was warned by Turkish air radar units, in both English and Russian, before it crossed into Turkish airspace from Syria on Friday.
The statement went on to warn that violations "could lead to serious consequences."
The Russian Defense Ministry denied that it violated Turkish airspace and called Ankara's allegations "unfounded propaganda.'
"There were no violations of Turkish airspace by planes of the Russian air group in the Syrian Arab Republic," the ministry said on Facebook.
The ministry said that the nationality of an aircraft cannot be established on radar.
"This is only possible through direct visual contact from another aircraft, which did not take place," the ministry emphasized.
Turkey's military shot down a Russian plane in November after it ignored several warnings and entered its airspace, according to Turkish officials. One Russian crew member was killed. Moscow disputed that its crew was given warnings before the F-16 fired and said the Russian plane was over Syria.
After the shootdown, Russia imposed a series of economic sanctions on Turkey, banning the import of some goods, imposing restrictions on travel, barring some Turkish companies from doing business in Russia and suspending a $12 billion gas pipeline project between the nations.
NATO Secretary-General Jens Stoltenberg called Saturday for "calm and de-escalation."
But he also said Russia should "act responsibly and to fully respect NATO airspace."
An official with the Russian Embassy in Ankara confirmed there was a meeting, Ria Novosti reported, but spokesman Igor Mityakov declined to comment on what was discussed.
Russia began airstrikes in Syria, one of Turkey's neighbors to the south, in September. Moscow has said the missions are in support of the Syrian government's fight against ISIS and other enemies.
The officials said the United States had seen a "limited" number of Russian military personnel, more akin to an exploratory party, looking at an airfield in Qamishli, possibly to determine how they might use the site.