Turkey has shot down a Russian fighter plane near the Syrian border in an incident described by Vladimir Putin as a "stab in the back by the terrorists' accomplices".

The incident, in which at least one of two pilots died, marks the first time in half a century that a Nato member has downed a Russian plane.

The long-feared incident highlighted the growing complexity of Syria's civil war, as multiple groups with clashing alliances fight on the ground and the sky is crowded with aircraft bombing various targets.

It immediately prompted fierce reaction from Moscow. Russian president Mr Putin called Turkey's action a "stab in the back by the terrorists' accomplices" and warned of "significant consequences".

Meanwhile Russian foreign minister Sergey Lavrov cancelled a trip to Turkey which had been planned for Wednesday.

Nato secretary-general Jens Stoltenberg called on all parties to be prudent and to contribute to reducing tensions.

"As we have repeatedly made clear we stand in solidarity with Turkey and support the territorial integrity of our Nato ally, Turkey," Mr Stoltenberg said after an extraordinary meeting of the alliance's decision-making North Atlantic Council, called at Turkey's request.

He called for "calm and de-escalation", and renewed contacts between Moscow and Ankara.

Turkey said two SU-24 planes ignored several warnings that they were nearing, and then intruding into, Turkish airspace. In a letter to the UN Security Council and secretary-general Ban Ki-moon, it said the planes disregarded warnings and violated Turkish airspace "to a depth of 1.36 miles and 1.15 miles in length for 17 seconds" just after 9.24am local time.

It said one of the planes then left Turkish airspace and the other one was fired at by Turkish F-16s "in accordance with the rules of engagement" and crashed on the Syrian side of the border.

Russia insisted the plane stayed over Syria, where it was supporting ground action by Syrian troops against rebels.

Rebel forces fired at the two parachuting pilots as they descended, and one died, said Jahed Ahmad, a spokesman for the 10th Coast Division rebel group. The fate of the second pilot was not immediately known.

Later on Tuesday, Russia's military said that one of two of its helicopters that were searching for the jet's crew in Syria was shot down by rebel fire and one serviceman was killed. The rest of its crew were evacuated and taken back to the air base used by Russia in Syria.

A US defence official in Washington DC confirmed the Russian plane entered Turkish airspace before Turkey shot it down. The official said the Russian plane flew across a two-mile section of Turkish airspace, meaning it was in Turkish airspace only for a matter of seconds.

Turkey and Russia have long been at odds over the crisis in Syria, where Turkey has been seeking the ouster of President Basher Assad - an important Russian ally.

Turkey has also voiced concerned over Russia's bombing of Turkmen areas in Syria and the fact that the Russian operations have complicated the possibility of creating a safe zone in northern Syria to protect civilians as well as moderate rebels fighting Assad. The creation of a safe zone has been a long-term Turkish goal.

Mr Putin said: "We will never tolerate such atrocities as happened today and we hope that the international community will find the strength to join forces and fight this evil."

Turkish prime minister Ahmet Davutoglu insisted his country has the right to take "all kinds of measures" against border violations, and called on the international community to work toward "extinguishing the fire that is burning in Syria".

But despite the harsh words, some analysts believe that Russia and Turkey have reasons not to let the incident escalate.

Natasha Kuhrt, lecturer in international peace and security at King's College London, said: "Relations have been very strained between Russia and Turkey of late so Moscow will be trying its utmost to contain the damage this might cause."

Ian Kearns, director of the London-based think-tank European Leadership Network, said: "It's a serious incident in anybody's book."

But Mr Kearns said the Russian-Turkish economic relationship, including in the energy field, is important to Moscow.

And Russia and the West appeared to be moving toward an understanding of their common strategic interest in eradicating Islamic State (IS, also known as Isil) following the bombing of a Russian airliner over Sinai on October 31 and the November 13 attacks in Paris.

A Turkish military statement said the Russian plane entered Turkish airspace over the town of Yayladagi, in Hatay province.

Turkish officials released what they said was the radar image of the path the Russian plane took, showing it flying across a stretch of Turkish territory in the country's southern-most tip.

Colonel Steve Warren, spokesman for the US military in Baghdad, said the US heard communication between Turkish and Russian pilots and could confirm that Turkish pilots issued 10 verbal warnings before the plane was shot down.

The Russian plane was supporting Syrian troops which have been on the offensive in an area controlled by several insurgent groups including al Qaida's branch in Syria, the Nusra Front, and the 2nd Coastal Division and the 10th Coast Division that include local Turkmen fighters.