Obama and Erdogan at the G20 summit on November 15. Photo by EPA

US President Barack Obama has stepped into the ongoing feud between Turkey and Russia, saying on Tuesday he supported Turkey's right to defend itself.

Speaking after a meeting with Turkish counterpart Recep Tayyip Erdogan in Paris, where he has been attending the climate summit, Obama said "The United States supports Turkey's right to defend itself and its air space."

The two leaders discussed "how Turkey and Russia can work together to de-escalate tensions" and find a diplomatic path to resolve the issue, he said.

A war of words has continued to rumble between Turkey and Russia since Turkish F-16s shot down a Russian warplane along the Syrian border last week.

Turkish President Recep Tayyip Erdogan challenged his Russian counterpart Vladimir Putin on Monday to prove his claims that Turkey shot down the jet because it wanted to protect supplies of oil from Islamic State militants.

Speaking to reporters at the United Nations summit, Erdogan said such claims were "slander" and said he would resign if they were proved true — before throwing the gauntlet back to Putin.

"We are not that dishonest as to buy oil from terrorists," he said. "As soon as such a claim is proved, the nobility of our nation requires [me] to do this, I will not remain in this post. But I am asking Mr Putin, would you remain?"

The two leaders did not meet on Monday at the summit which Erdogan had previously described as an opportunity to mend shattered ties between the two countries.

Aides to Putin say he is incandescent that Erdogan has yet to apologize for the downing of the SU-24 jet in which one Russian pilot was killed along with a Russian marine who tried to rescue the crew.

Moscow approved a raft of economic sanctions against Turkey over the weekend, and said on Monday said it would ban mainly imports of mainly imports of agricultural products, vegetables and fruits from Turkey and may expand its sanctions if needed.

A few hours later 1,250 trucks carrying Turkish exports were blocked from entering Russia and were stranded at border posts awaiting clearance.

"Let's act patiently and not emotionally," Erdogan told reporters when asked whether Turkey would hit back with its own sanctions. "Let's let their chips fall as they may, then if we have our own chips, we'll let those fall."

Turkish Prime Minister Ahmet Davutoglu struck a more conciliatory tone on Tuesday, calling for the opening of communication channels between Turkey and Russia.

"Our call to Russia again is to open military communication channels to prevent similar incidents happening. Let's keep diplomatic channels open," Davutoglu told a news conference before departing on an official visit to northern Cyprus.

Turkish officials have said the Russian jet violated Turkish airspace and had been warned repeatedly. Moscow says the aircraft was over Syria, where Russia is carrying out an air campaign to support the forces of President Bashar al-Assad in a four-year-old civil war.

Erdogan is among Assad's most outspoken critics, and Russia's bombardment of certain opposition groups in Syria has put Ankara and Moscow at odds. Erdogan has said Turkey will not apologise for the downing of the plane.

The president of the Syrian Turkmen Assembly, which represents the Turkmen ethnic minority in northwestern Syria, told the Independent that Moscow was deliberately bombing the region where his people lived in order to "drive [them] out" as part of an attempt to carve up the country and create a safe enclave for al Assad.