Russia’s defence ministry said an Su-24 had crashed on Syrian territory after being hit by fire from the ground, and that its pilots had managed to eject.
But Turkish military officials said Turkish F-16s had shot down the plane after repeatedly warning its pilots they were violating Turkish airspace.
Video footage showed the plane crashing into mountains in Latakia province.
Russia launched an air campaign to bolster Syrian President Bashar al-Assad’s government in late September.
The Russian defence ministry confirmed on Tuesday morning that a Russian Su-24 had “crashed on Syrian territory, having been hit from the ground” while it was flying at an altitude of 6,000m (19,685ft).
“Efforts are being made to ascertain what happened to the pilots. According to preliminary reports, the pilots have managed to self-eject,” the ministry was quoted as saying by the Interfax news agency.
The ministry stressed that “throughout its flight, the aircraft remained exclusively above Syrian territory”, adding: “This has been recorded by objective means of control.”
However, Turkish military officials said its F-16s had fired on an unidentified military aircraft after warning it 10 times in the space of five minutes about violating Turkish airspace.
The Syrian Observatory for Human Rights, a UK-based monitoring group, said the warplane crashed in a mountainous area of Latakia province, where air strikes and fighting between rebels and Syrian government forces had been reported earlier on Tuesday.
Qatar-based Al Jazeera TV quoted an ethnic Turkmen rebel group as saying it had captured one of the Su-24’s two pilots and were “looking for the other”.
Russian aircraft have flown hundreds of sorties over northern Syria since September. Moscow says they have targeted only “terrorists”, but activists say its strikes have mainly hit Western-backed rebel groups.
Turkey, a staunch critic of Mr Assad, has warned against violations of its airspace by Russian and Syrian aircraft.
Last month, Ankara said Turkish F-16s had intercepted a Russian jet that crossed its border and two Turkish jets had been harassed by an unidentified Mig-29.