The shooting down of a Russian jet by Turkey is a "stab in the back" committed by "accomplices of terrorists", Vladimir Putin has said.

The Sukhoi Su-24 was warned 10 times before being downed near the Syrian border by two Turkish F16 jets for violating the country's airspace, according to the Turkish military.

A Turkish official said two Russian planes approached the Turkish border and were warned before one of them was shot down, adding their information shows Turkish airspace was repeatedly violated.

A US official has said initial indications are that the incursion into Turkish airspace lasted a matter of seconds.

It has triggered a major diplomatic confrontation, with NATO calling an emergency meeting to discuss the incident.

There are conflicting reports about the fate oft the two pilots.

Russia confirmed one of the pilots was killed by groundfire as he parachuted from the plane.

But a Turkish official has told Reuters news agency Turkey believes the two pilots are still alive and is working to secure their release from Syrian rebels.

However, a rebel group has said it shot dead the two pilots as they tried to land safely in northern Syria after ejecting from the jet.

Video sent to Reuters appears to show one of the pilots immobile on the ground. "A Russian pilot," a voice is heard saying, as men gather around the man on the ground. "God is great," is also heard.

Sky News Foreign Affairs Editor Sam Kiley said claims the pilots are still alive "is in direct contradiction with what the Turkish-speaking rebels on the ground have said".

"This may be good news for the families if they have survived - but we have seen published videos of what appears to be the bodies of two different men ... I think the assumption remains (they are dead) and that the Turks might be a little bit behind with their information," he said.

A Russian soldier was also killed while searching for the pilots after his helicopter was shot at in Syria, the Russian military said.

A military spokesman said the shooting killed one crew member on the Mi-8 helicopter.

Video emerged earlier purporting to show Syrian rebel fighters who have received US arms destroying a Russian helicopter while it was on the ground.

It is unclear whether it is linked to the death of the soldier searching for the pilots.

The downing of the jet is the first time a NATO member's armed forces have shot down a Russian or Soviet military aircraft since the 1950s.

The Russian leader said the jet "did not in any way threaten Turkey" and the incident will have "serious consequences" for relations between the two countries.

Mr Putin said the aircraft was shot by a missile from a Turkish jet over Syria around 1km (just over half a mile) away from the Turkish border, which he described as a "stab in the back by the terrorists' accomplices".

Foreign minister Sergei Lavrov has cancelled a trip to Turkey scheduled for Wednesday and advised Russians not to visit the country.

Turkish Prime Minister Ahmet Davutoglu said his country has a right to respond if its airspace is violated, and stressed the action was not an act of aggression against any foreign territory.

Following the extraordinary meeting, NATO secretary general Jens Stoltenberg called for "calm and de-escalation" and said the allies "stand in solidarity with Turkey".

US President Barack Obama said Turkey "has a right to defend its territory and its airspace", but urged both Turkey and Russia to take measures "to discourage any kind of escalation".

He said Russia should be doing more to target Islamic State with its airstrikes in Syria, instead of striking moderate opposition groups to bolster President Bashar al Assad's regime.

He said Russia concentrated on bombing IS, then mistakes would be "less likely to occur".

Russia's defence ministry summoned Turkey's military attache in Moscow for an official protest. The attache was presented with a document say the jet downing was "unfriendly action".

And Russia's charge d'affaires has been summoned to the Turkish foreign ministry.

The Russian plane went down in an area known by Turks as "Turkmen Mountain" in northern Syria near the Turkish border.

The region has been the subject of a Syrian government offensive in recent days under the cover of Russian airstrikes.

Turkey has previously called for a UN Security Council meeting to discuss attacks on Turkmens in Syria.

Last week Ankara summoned the Russian ambassador to protest against the bombing of the villages by Moscow, saying Russia's actions did not "constitute a fight against terrorism" but the bombing of civilians.

Turkey has traditionally expressed solidarity with Syrian Turkmens, who are Syrians of Turkish descent.

TV footage broadcast showed a plane going down in flames in a woodland area, with a long plume of smoke trailing behind it: