A Russian marine has been killed on a helicopter mission to rescue the crew of a jet downed by Turkey near the Syrian border on Tuesday.

He died when his helicopter came under fire from rebels in northern Syria, where the plane crashed.

Rebel fire from the ground killed one of the jet's two crew members after they ejected.

The head of Nato said it stood in solidarity with Turkey as the Kremlin warned of "serious consequences".

US President Barack Obama later assured his Turkish counterpart, Recep Tayyip Erdogan, in a phone call of US support for his country's right to defend its sovereignty.

The White House said both presidents had agreed on the importance of de-escalating the situation.

Turkey said the jet had strayed into its airspace but Russian President Vladimir Putin insisted the Su-24 had been hit by an air-to-air missile while flying over Syrian territory.

Nato's Secretary General Jens Stoltenberg said he backed the Turks' assessment.

"We stand in solidarity with Turkey and support the territorial integrity of our Nato ally, Turkey,'' he said after an emergency meeting of the bloc.

He also called for both sides to de-escalate the situation.

President Putin described the downing of the plane as a "stab in the back".

Breaking off military contacts with Turkey, Russia's defence ministry said a cruiser equipped with an air defence system would be deployed in the Mediterranean to destroy "any targets representing a potential danger" for Russian forces in Syria.

Russian bombers carrying out air strikes over Syria will now be escorted by fighters, the military said.

Analysis: Mark Lowen, BBC Turkey correspondent

After Turkey became the first Nato member to shoot down a Russian plane in over half a century, the question now is how will Moscow respond?

President Putin called Turkey an "accomplice of terrorists" and Foreign Minister Sergei Lavrov cancelled a planned trip to Ankara on Wednesday.

But the UN and Nato have urged both sides to de-escalate the crisis. According to Ankara, the Russian Su-24 was warned ten times about entering Turkish airspace, though Moscow says there was no such communication.

But Turkey also said the violation lasted just seventeen seconds. And given signs that a united front was beginning to form against Islamic State, there will be diplomatic pressure on both sides to focus instead on the common threat from the militants.

The tough talk from Ankara and Moscow will no doubt continue - but whether there will be serious retaliation is less clear.

Russian defence official Lt-Gen Sergey Rudskoy said the rest of the rescue team, which were using two Mi-8 helicopters, had been safely evacuated from the area to Russia's Humaymim air base near Latakia in Syria.

"During the operation, one of the helicopters came under small-arms fire, was damaged and made an emergency landing on neutral territory," he said.

"One naval infantryman serving under contract was killed."

One of the helicopters was destroyed on the ground by "mortar fire" after making an emergency landing, the Russian general said.

Syrian rebels say they blew up the helicopter shortly after it landed with an anti-tank missile, releasing footage of the attack.

The fate of the Russian jet's other crew member remains unknown.

Russians have been advised not to visit Turkey - a popular tourist destination - with Foreign Minister Lavrov saying the terror threat there was no less than in Egypt, where a bomb attack brought down a Russian passenger plane last month.

One of Russia's largest tour operators, Natali Tours, has suspended package holidays to Turkey.

There are loud calls in Russia for economic sanctions and for all flights to Turkey to be cancelled, the BBC's Moscow correspondent, Sarah Rainsford, reports.

The Turkish president said his forces had been acting within their rules of engagement.

"Everyone must respect the right of Turkey to protect its borders," he said.

The US, the EU and the UN have all appealed for calm.

President Obama said it was important to find out exactly what had happened and to take measures to "discourage any kind of escalation".

But he said the incident pointed to an "ongoing problem" with Russian action in Syria, saying if Russia had been targeting IS, rather than "moderate" Syrian opposition forces, such incidents would be unlikely.

Russia and Turkey have found themselves on opposing sides in Syria's conflict, with Russia supporting its ally President Bashar al-Assad and Turkey calling for his ousting.