Russia on Wednesday accused Turkish President Recep Tayyip Erdogan and his family of involvement in illegal oil trading with Islamic State jihadists, ratcheting up the heat in a dispute over Ankara's downing of one of Moscow's warplanes.

The Turkish strongman accused Moscow of "slander" over claims his country had bought oil from IS, while Russian Foreign Minister Sergei Lavrov agreed to meet his counterpart from Ankara for the first high-level face-to-face talks since the ferocious war of words erupted last week.

Ties between NATO member Turkey and Russia have been strained since Ankara shot down the jet on its border with Syria on November 24, with President Vladimir Putin accusing Ankara of downing the jet to protect oil supply lines to Turkish territory.

But the defence ministry accusations against Erdogan are the first implicating the Turkish strongman directly.

"The main consumer of this oil stolen from its legitimate owners Syria and Iraq is Turkey," deputy defence minister Anatoly Antonov told journalists.

"According to available information, the highest level of the political leadership of the country, President Erdogan and his family, are involved in this criminal business."

- 'Fantastic family business' -

Erdogan angrily dismissed Russian claims that Ankara is trading in oil with jihadist groups, insisting he would resign if allegations were proved true.

"No one has a right to engage in slander against Turkey by saying that Turkey is buying oil from Daesh (IS)," he said on a visit to Ankara's closest ally Qatar, where he signed a memorandum of understanding on gas supplies.

The Russian briefing broadcast satellite images of oil trucks on a huge screen but did not provide any specific data on how Erdogan is tied to the activities.

Antonov pointed the finger at the recent appointment of Erdogan's son-in-law Berat Albayrak as energy minister and alleged that the president's son runs one of the country's main energy companies.

"What a fantastic family business," he said, claiming that "terrorists" in Syria make some $2 billion (1.9 billion euros) each year out of the illegal oil trade.

Still Lavrov agreed to meet his Turkish counterpart Mevlut Cavusoglu in Belgrade later this week for the first time since the downing.

"We will not be evading this contact," Lavrov said during a visit to Cyprus.

"We will hear what Mr Cavusoglu has to say. Perhaps there will be something new after what has already been said publicly."

After arriving in Belgrade, he told reporters that it would be "sad not to hear anything new" from the Turkish side.

- Threat of sanctions response -

Putin snubbed a meeting with Erdogan at the UN climate conference in France on Monday, after Lavrov had earlier scrapped a visit to Istanbul just after the plane downing.

Erdogan has rejected Putin's demands to apologise over the incident, saying that Turkey was acting well within its rights to protect its border.

Ankara claims the plane was in its airspace and ignored repeated warnings but Moscow insists it never crossed the border from Syria.

US President Barack Obama on Tuesday met Erdogan and called on both leaders to end their dispute and focus on fighting IS.

Turkey and Russia are close economic partners, with Moscow the main supplier of oil and gas to the energy-poor country.

But they are rival players in the war in Syria, with Ankara part of a US-led coalition against IS that is opposed to President Bashar al-Assad while Moscow has launched a bombing campaign at the request of the Damascus regime.

Moscow has announced an embargo on some Turkish food imports and halted the sale of package holidays there in a bid to punish Ankara.

Erdogan said Turkey was pushing for a diplomatic resolution for the crisis.

"We are saddened by the disproportional responses by Russia to an incident in which the whole world agrees we are right," Erdogan said.

"If these responses continue we will take our own measures," he added, without elaborating.

While Turkey and Russia continued to wrangle, the body of a pilot killed when the jet was blown out of the sky was buried in his hometown some 360 kilometres south of Moscow.

Local media reported that thousands of mourners flocked to bid farewell to Oleg Peshkov, who the defence ministry said was shot dead from the ground after parachuting out of the jet.

The corpse of the pilot -- who has been awarded Russia's highest honour -- was flown back from Turkey after it was taken across the border from Syria.