Turkey 'has the right to defend its territory and airspace' - Obama
* Obama's comments follow downing of Russian warplane
* Turkey claim plane invaded its airspace
* Russia say they can prove plane was in Syrian airspace
* NATO calls for 'cool-headedness'
US President Obama has said Turkey 'has the right to defend its territory and airspace'.
President Obama's comments come after Turkish fighter jets shot down a Russian warplane near the Syrian border after repeated warnings over air space violations.
Moscow has since said it could prove the jet had not left Syrian air space.
It was the first time a NATO member's armed forces have downed a Russian or Soviet military aircraft since the 1950s and Russian and Turkish assets fell on fears of an escalation between the former Cold War enemies.
NATO ambassadors called on the Turkish capital Ankara to show "cool-headedness" on Tuesday following an emergency meeting in Brussels.
Diplomats present at the meeting told Reuters that while none of the 28 NATO envoys defended Russia's actions, many expressed concern that Turkey did not escort the Russian warplane out of its airspace.
"There are other ways of dealing with these kinds of incidents," said one diplomat who declined to be named.
Meanwhile, a Kremlin spokesman said it was a "very serious incident" but that it was too early to draw conclusions.
President Vladamir Putin warned that the incident would have 'serious consequences' for Russia-Turkey relations.
He added that the downing of the war plane is a "stab in the back" from Turkey.
However Turkish prime minister Ahmet Davutoglu says he asserts the right to take "all kinds of measures" against border violations.
Footage from private Turkish broadcaster Haberturk TV showed the warplane going down in flames in a woodland area, a long plume of smoke trailing behind it. The plane went down in area known by Turks as "Turkmen Mountain", it said.
Separate footage from Turkey's Anadolu Agency showed two pilots parachuting out of the jet before it crashed.
Syrian fighters fired at a Russian helicopter forcing it to make an emergency landing in a nearby government-held area in Syria's Latakia province on Tuesday, the Syrian Observatory for Human Rights said.
The helicopter was attempting a rescue operation in the area.
A Syrian insurgent group, recipient of U.S. Tow missiles, said its fighters hit the helicopter with an anti-tank missile.
Russia's defence ministry said one of its Su-24 fighter jets had been downed in Syria and that, according to preliminary information, the pilots were able to eject. It said the aircraft had been over Syria for the duration of its flight.
The Turkish military said the aircraft had been warned 10 times in the space of five minutes about violating Turkish airspace. Officials said a second plane had also approached the border and been warned.
"The data we have is very clear. There were two planes approaching our border, we warned them as they were getting too close," a senior Turkish official told Reuters.
"We warned them to avoid entering Turkish airspace before they did, and we warned them many times. Our findings show clearly that Turkish airspace was violated multiple times. And they violated it knowingly," the official said.
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Russia's unilateral decision to launch air strikes in Syria mean 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 main stock index fell more than two percent, while Turkish stocks fell 1.3 percent. Both the rouble and lira were weaker.
Turkish President Tayyip Erdogan was briefed by the head of the military, while Prime Minister Ahmet Davutoglu ordered consultations with NATO, the United Nations and related countries, their respective offices said.
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.
Islamic State, which has beheaded foreign captives in the past, is not known to have a presence there.
One of the pilots was in the hands of Turkmen forces in Syria who were looking for the other one, broadcaster CNN Turk reported, citing local sources. Russian military helicopters were also searching for the pilots, Turkey's Dogan news agency reported.
Both Russia and its ally, Syria's government, have carried out strikes in the area. A Syrian military source said the reported downing was being investigated.
Turkey called this week for a U.N. Security Council meeting to discuss attacks on Turkmens in neighbouring Syria, and last week Ankara summoned the Russian ambassador to protest the bombing of their villages.
Ankara has traditionally expressed solidarity with Syrian Turkmens, who are Syrians of Turkish descent.
Russian Foreign Minister Sergei Lavrov is due to visit Turkey on Wednesday to discuss Syria, in a trip arranged before this incident. Erdogan is meanwhile expected to visit Russia for talks with Putin in late December.
About 1,700 people have fled the mountainous Syrian area near to the Turkish border as a result of 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.