Russian president Vladimir Putin has called Turkey's decision to down a Russian war plane near the Syria border a "stab in the back".
One of the pilots was dead upon landing after being shot at while descending in his parachute, according to a spokesman for the rebel group that captured him.
Speaking at a meeting with Jordanian King Abdullah II, Mr Putin accepted the king's condolences on the death of a Russian pilot who was reportedly captured and dead.
Mr Putin said the Russian SU-24 jet was shot by a missile from a Turkish jet over Syria about one kilometre (just over half a mile) away from the Turkish border, which he described as a "stab in the back by the terrorists' accomplices".
He warned that the incident would have "significant consequences" for its relations with Turkey and criticised Ankara for turning to Nato to discuss the incident instead of first explaining to Russia what happened.
Jahed Ahmad, of the 10th Brigade in the Coast, said the plane's two Russian crew members tried to land in their parachutes in Syrian government-held areas after they ejected, but came under fire from members of his group.
He added that rebels shot one of the pilots, who landed dead on the ground. The fate of the second pilot was not immediately known.
Speaking to Reuters, the group said footage showing a dead man in apparent Russian air force gear was genuine, and captured on Tuesday in the northern countryside of Latakia province.
The video, which has not been independently verified, appeared to show Syrian rebel fighters standing around the body and chanting "Allahu Akbar".
The Russian defence ministry denied that the plane crossed the Syrian border into Turkish skies.
It said: "We are looking into the circumstances of the crash of the Russian jet.
"The Ministry of Defence would like to stress that the plane was over the Syrian territory throughout the flight."
Russia said the Su-24 was downed by artillery fire, but Turkey claimed that its F-16s fired on the Russian plane after it ignored several warnings.
The ministry said the pilots parachuted but added that Moscow had no further contact with them.
Video footage of the incident showed a war plane on fire before crashing on a hill and two crew members apparently parachuting safely.
Two Russian helicopters, flying low over the Turkmen Bayirbucak region, searched for the two pilots, Turkish news agency Dogan said.
A Turkish military statement said the plane entered Turkish airspace over the town of Yayladagi, in Hatay province.
"On November 24 2015 at around 9.20am, a plane whose nationality is not known violated the Turkish airspace despite several warnings (10 times within five minutes) in the area of Yayladagi, Hatary," the military said before the plane's nationality was confirmed.
"Two F-16 planes on aerial patrol duty in the area intervened against the plane in question in accordance with the rules of engagement at 9.24am."
Turkey's foreign ministry summoned the Russian ambassador on Friday demanding that Russia cease operations in Syria targeting Turkmen villages, saying the Russian actions did not "constitute a fight against terrorism" but the bombing of civilians.
Ambassador Andrey Karlov was warned during the meeting that the Russian operations could lead to serious consequences, the ministry said.
Syrian troops have been on the offensive in the area that is controlled by several insurgent groups including al-Qaida's branch in Syria, the Nusra Front, and the 2nd Coastal Division that consists of local Turkmen fighters.
Rami Abdurrahman, who heads the Britain-based Syrian Observatory for Human Rights, said the war plane crashed in the Turkmen Mountains region in the coastal province of Latakia.
The Turkmen Mountains region has been subjected to a government offensive in recent days under the cover of Russian airstrikes.