Russia has insisted the downing of one of their warplanes by Turkey was "pre-planned".
As tensions rise between the two countries, the Russian pilot who survived the crash claims he was given no warning before his plane was shot down.
While Turkey claims it issued repeated warnings to the aircraft.
The Turkish Embassy in Moscow has since been targeted by protesters throwing eggs, tomatoes and stones.
ITV News Europe Editor James Mates reports:
The US Secretary of State has urged for calm between Turkey and Russia after the downing of a Russian warplane near the Syrian border.
John Kerry "stressed the need for both sides not to allow this incident to escalate tensions between their two countries or in Syria".
The downing of the Russian jet earlier this week was one of the most serious publicly acknowledged clashes between a NATO member and Russia for 50 years.
A Russian pilot who survived the downing of his plane said Turkish jets did not issue any warnings beforehand.
Captain Konstantin Murakhtin maintained his aircraft was flying over Syrian territory and did not violate Turkish airspace.
Mr Murakhtin was rescued and is currently at a Russian air base in Syria but his co-pilot was reportedly killed by militants on the ground.
He added that he wants to keep flying missions from the base "to pay them back for my commander".
Russian forces are reportedly unleashing a wave of air strikes on mountains near where the plane was shot down.
Mr Murakhtin said this was proving cover for advancing Syria ground forces and their Lebanese Hezbollah allies.
Air defence missile systems will be sent to Russia's air base in Syria, government leaders have said.
After a Russian fighter jet was shot down by Turkey amid allegations the Russians had violated their airspace, news agencies reported President Vladimir Putin as saying advanced, long-range anti-aircraft surface-to-air S-300 missile system would be deployed to the region.
Meanwhile, Defence Minister Sergei Shoigu said the newer version - the S-400 missiles - would be sent, to be stationed at Hemeimeem air base from where Russia is conducting its aerial bombing campaign in Syria.
Putin also accused Turkey's political leaders of supporting a "deliberate policy of Islamisation" of the country, saying he believed that was part of the problem.
Turkey needs to do everything it can to de-escalate the situation with Russia after shooting down one of its fighter jets, German Chancellor Angela Merkel has warned.
The incident has "complicated" the process of finding a political solution in Syria, she added, speaking in the lower house of parliament.
The situation has been aggravated by the shooting down of a Russian plane by Turkey.
We need to do everything to avoid an escalation. Of course every country has a right to defend its territory, but on the other hand we know how tense the situation is in Syria and in the surrounding area.
I spoke yesterday with the Turkish prime minister and asked him to do everything to de-escalate the situation.
Turkey does not want any "escalation" after shooting down a Russian fighter jet, President Tayyip Erdogan said - arguing his country had simply acted to defend its own security and the "rights of our brothers" in Syria.
Speaking at a business event in Istanbul, he insisted that the jet had been shot at while in Turkish air space, but said it had crashed inside Syria.
Some parts of the plane landed in Turkey and injured two citizens, he added.
One of two Russian pilots whose plane was shot down by Turkey has been picked up by the Syrian army and taken to Russia's base, officials have said - but the other has reportedly been killed by militants on the ground.
According to Russia's ambassador to France, he had managed to eject and escaped alive. He is now expected to be taken to the Russian airforce base in the country.
Speaking to Europe 1 radio, ambassador Alexandre Orlov said the other had been wounded when he parachuted down, and was then killed by militants.
One on board was wounded when he parachuted down and killed in a savage way on the ground by the jihadists in the area and the other managed to escape and, according to the latest information, has been picked up by the Syrian army and should be going back to the Russian airforce base.
The United States believes that the Russian jet shot down by Turkey was hit while flying over Syria after a brief incursion in Turkish airspace, an official has told Reuters.
The US official said the assessment was based on the jet's heat signature.
Barack Obama and Turkish President Tayyip Erdogan spoke by phone on Tuesday about the need to de-escalate tensions with Russia following the incident.
President Obama expressed "support for Turkey's right to defend its sovereignty," a White House spokesman said.
"The leaders agreed on the importance of de-escalating the situation and pursuing arrangements to ensure that such," they added.
Tensions between Turkey and Russia increased today after a Russian warplane was shot down after entering Turkey's airspace near the border with Syria.
It's now believed that both Russian pilots shot down near the Turkey/Syria border have been killed.
Nato and the United Nations have called for calm and have urged both nations to de-escalate the situation.
ITV News Europe Editor James Mates reports:
Confusion still surrounds the fate of the two Russian pilots shot down after their SU-24 attack jet briefly entered Turkish airspace.
Authorities in Turkey say that the two aircrew are thought to be alive and that the government is attempting to recover them.
But the Russian military say at least one the pilots was shot and killed by troops as he parachuted from the wreck. They also say a marine was killed when a helicopter looking for the downed crew was attacked.
Earlier, Turkmen rebels along the Turkish/Syria border claimed that they shot the men as they fell to earth via parachute.
Both of the pilots were retrieved dead.
Our comrades opened fire into the air and they died in the air.