Turkey shot down a Russian war plane on the Syrian border, sending tensions spiralling as Russian President Vladimir Putin warned Ankara its "stab in the back" would have serious consequences.

NATO chief Jens Stoltenberg said the military alliance stood by member Turkey after the incident, but echoed appeals for calm from other world leaders as fears grow of clashes between coalition and Russian planes in the skies over Syria.

"We stand in solidarity with Turkey and support the territorial integrity of our NATO ally, Turkey," Stoltenberg said after an emergency meeting of all 28 members requested by Ankara.

Russia has been carrying out strikes over Syria since late September and Turkey has warned it would act if the country's jets continued to enter its air space ©Sergey Venyavsky (AFP)

"Diplomacy and de-escalation are important to resolve this situation," added.

Turkey's military said the fighter was shot down by two of its F-16s after it violated Turkish airspace 10 times within a five-minute period.

The Turkish Ambassador to the United Nations Halit Cevik said in a letter to the Security Council that two Russian planes had flown a little more than a mile into Turkish airspace for 17 seconds.

But Moscow bitterly criticised Turkey for downing the Su-24 plane, which it insisted was in Syrian airspace, and claimed that one of the two pilots who ejected from the craft was killed by gunfire from the ground as he descended.

The second pilot "was picked up by the Syrian army", Russia's ambassador to France said Wednesday.

"(He) managed to escape and according to the latest information we have, he was picked up by the Syrian army and will be taken to the Russian airbase," Alexander Orlov told Europe 1 radio.

Putin branded the shooting down of the aircraft a "stab in the back committed by accomplices of terrorists", warning: "The tragic event will have serious consequences for Russian-Turkish relations."

Russian Foreign Minister Sergei Lavrov scrapped a planned visit to Turkey Wednesday, and warned Russians against travelling to Turkey.

He said the risk of attacks "is no less of a threat than in Egypt," where all 224 people onboard a Russian passenger jet were killed in October in an attack claimed by the Islamic State.

Russia's Moskva guided missile cruiser will now be stationed near Latakia, on Syria's Mediterranean border, and all bombers in Syria will now be escorted by fighters, Russian military spokesman General Sergei Rudskoi said, adding the shooting down would have the "the gravest consequences".

"All targets representing a potential threat to us will be destroyed," he warned.

- 'Flagrant aggression' -

While Russia and Turkey have traded barbs before over alleged incursions by Russian fighters into Turkish airspace during forays over Syria, this is the first time Turkey has shot down any Russian planes since Moscow started airstrikes in September.

The incident has sparked concern in the West it could escalate into clashes between Russian and other members of the US-led coalition, which include Turkey, during their separate campaigns to target jihadists in Syria.

It also risks derailing efforts to bring peace to Syria that were gaining tentative momentum following the November 13 Paris terror attacks, claimed by militants from the Islamic State group, which controls swathes of northern Syria.

Damascus, an ally of Moscow, denounced the incident as "flagrant aggression" against Syrian sovereignty.

A US military spokesman in Baghdad confirmed Turkey had warned the Russian jet 10 times, without response, before shooting it down but said it was not immediately clear on which side of the border the jet had been flying.

US President Barack Obama called for calm, saying his top priority "is going to be to ensure that this does not escalate".

He echoed that sentiment in a phone call with his Turkish counterpart, in which President Recep Tayyip Erdogan's office said Obama had also backed Ankara's right to defend the country's sovereignty.

- Jet 'no threat to Turkey' -

Putin said the plane fell in Syrian territory four kilometres (2.5 miles) from the border and "did not in any way threaten Turkey".

The incident comes as Russian and Syrian jets wage a heavy bombing campaign against targets in northern Syria.

Turkey has expressed anger at the operation, saying it is aimed at buttressing the Assad regime and has displaced thousands of Turkmen Syrians, an ethnic minority in the area and strong allies of Ankara.

UN Secretary-General Ban Ki-moon called for a "credible and thorough review" of the incident to establish what happened and ensure it does not happen again.

Meanwhile, the fate of the second pilot in the plane remained unclear.

Turkish television pictures showed the Su-24 exploding and crashing in a ball of flames into a Syrian mountain and two pilots parachuting to the ground after ejecting.

A Turkish government official insisted both pilots were still alive, but Russian military spokesman Rudskoi said one was killed by fire from the ground after he ejected from the craft.

Rudskoi added a Russian soldier had also been killed in a failed bid to rescue the pilots when a Mi-8 helicopter was "damaged by gunfire and had to land".

Turkey shoots down a Russian warplane

Smoke billows from the spot where the Su-24 warplane crashed in Hatay