Russian President Vladimir Putin has warned of "serious consequences" after Turkey shot down a Russian warplane near the Syrian border on Tuesday, saying the jet had violated its air space, in one of the most serious publicly acknowledged clashes between a NATO member country and Russia for half a century.

Putin said the plane had been attacked when it was 1 km (0.62 mile) inside Syria and said the attack was a stab in the back administered by "the accomplices of terrorists".

"We will never tolerate such crimes like the one committed today," Putin said, as Russian and Turkish shares fell on fears of an escalation between the former Cold War enemies.

In a letter to the UN Security Council, Turkey said it had shot down the jet while in Turkish air space. Along with a second plane, the aircraft had flown more than a mile into Turkey for 17 seconds, despite being warned 10 times in five minutes while approaching to change direction, the letter said.

"Nobody should doubt that we made our best efforts to avoid this latest incident. But everyone should respect the right of Turkey to defend its borders," Turkish President Tayyip Erdogan said in a speech in Ankara.

In condemnation of Russian air strikes in Syria, during which Turkish air space has been violated several times in recent weeks, Erdogan said that only Turkey's "cool-headedness" had prevented worse incidents in the past.

Each country summoned a diplomatic representative of the other. Russia's Foreign Minister Sergei Lavrov canceled a visit to Turkey due on Wednesday and the defence ministry said it was preparing measures to respond to such incidents.

US President Barack Obama and French President Francois Hollande, meeting in Washington, urged against an escalation, while NATO Secretary-General Jens Stoltenberg said the military alliance stood in solidarity with Turkey.

Footage from private Turkish broadcaster Haberturk TV showed the warplane going down in flames, a long plume of smoke trailing behind it as it crashed in a wooded part of an area the TV said was known by Turks as "Turkmen Mountain".

Separate footage from Turkey's Anadolu Agency showed two pilots parachuting out of the jet before it crashed.

A deputy commander of rebel Turkmen forces in Syria said his men shot both pilots dead as they came down. The Russian military confirmed one pilot had been shot dead from the ground and another soldier died during a rescue operation.

A senior Turkish official said at least one of the pilots could still be alive. "It's not a fact but a possibility. We're trying to verify the information and taking all necessary steps to facilitate their return," the official said.

A video sent to Reuters earlier appeared to show one of the pilots immobile and badly wounded on the ground.

"Moral crusade"

Russia's defence ministry said one of its Su-24 fighter jets had been downed in Syria and that "for the entire duration of the flight, the aircraft was exclusively over Syrian territory", a suggestion Turkey denied.

"The data we have is very clear. There were two planes approaching our border, we warned them as they were getting too close," another senior Turkish official told Reuters. "Our findings show clearly that Turkish air space was violated multiple times. And they violated it knowingly."

A US military spokesman said it was an issue between the Turkish and Russian governments and that US-led coalition operations in Syria and Iraq were continuing "as planned".

Moscow's decision to launch separate air strikes in Syria means Russian and NATO planes have been flying combat missions in the same air space for the first time since World War Two, targeting various insurgent groups close to Turkish borders.

Russia's military involvement in Syria has brought losses, including the bombing by militants of a Russian passenger jet over Egypt. But there is no sign yet that public opinion is turning against the operation in Syria and the Kremlin said it would continue.

Instead Moscow, helped by state-controlled television, has used these reverses to rally public opinion, portraying the campaign as a moral crusade that Russia must complete, despite indifference or obstruction from elsewhere.

A US official said US forces were not involved in the downing of the Russian jet, which was the first time a Russian or Soviet military aircraft has been publicly acknowledged to have been shot down by a NATO member since the 1950s.

The incident appeared to scupper hopes of a rapprochement between Russia and the West in the wake of the Islamic State attacks in Paris, which had led to calls for a united front against the jihadist group in Syria.

Russia's main stock index fell more than two per cent, while Turkish stocks fell more than four per cent. Both the rouble and lira currencies were weaker.

Lavrov advised Russians not to visit Turkey and one of Russia's largest tour operators to the country said it would temporarily suspend sales of trips.

Shot as they fell

The Syrian Observatory for Human Rights monitoring group said the warplane crashed in a mountainous area in the northern countryside of Latakia province, where there had been aerial bombardment earlier and where pro-government forces have been battling insurgents on the ground.

"A Russian pilot," a voice is heard saying in the video sent to Reuters as men gather around the man on the ground. "God is great," is also heard.

The rebel group that sent the video operates in the northwestern area of Syria, where groups including the Free Syrian Army are active but Islamic State, which has beheaded captives in the past, has no known presence.

A deputy commander of a Turkmen brigade told reporters on a trip organised by Turkish authorities that his forces had shot both pilots dead as they descended.

"Our comrades opened fire into the air and they died in the air," Alpaslan Celik said near the Syrian village of Yamadi, holding what he said was a piece of a pilot's parachute.

In a further sign of a growing fallout over Syria, Syrian rebel fighters who have received US arms said they fired at a Russian helicopter, forcing it to land in territory held by Moscow's Syrian government allies.

Turkey called this week for a UN Security Council meeting to discuss attacks on Turkmens, who are Syrians of Turkish descent, and last week Ankara summoned the Russian ambassador to protest against the bombing of their villages.

About 1,700 people have fled the mountainous area due to fighting in the last three days, a Turkish official said on Monday. Russian jets have bombed the area in support of ground operations by Syrian government forces.