U.S. President Barack Obama called on Russia and Turkey to move beyond a furious row over the downing of a fighter jet and focus on the Islamic State jihadist group, after meeting his Turkish counterpart in Paris on Tuesday.

Relations between Moscow and Ankara have plummeted in the past week after Turkey downed a Russian fighter jet along the Syrian border.

Turkish Prime Minister Ahmet Davutoglu on Tuesday called on Russia to re-establish dialogue channels instead of making "baseless accusations" of an alleged oil trade between Ankara and Islamic State (IS) jihadists.

"We should sit at the table and discuss what to do instead of making baseless accusations," Davutoglu told reporters at Ankara airport before leaving for a visit to the Turkey-backed breakaway region of northern Cyprus.

Turkey on Saturday warned its citizens off non-urgent travel to Russia in the latest tit-for-tat move as the two nations square off over Ankara's downing of one of Moscow's warplanes.

The foreign ministry in Ankara said travel to Russia should be avoided a day after Moscow -- which had earlier urged its nationals to leave Turkey -- announced it was scrapping its visa-free regime for Turkish visitors.

Russia's Foreign Minister Sergei Lavrov on Friday said that Ankara has crossed the line by shooting down a Russian warplane this week and warned the incident could severely undermine Turkey's interests.

"We believe that the Turkish leadership has crossed the line of what is acceptable," Lavrov said at the start of talks with Syrian counterpart Walid Muallem in Moscow.

The Kremlin said Friday that Western powers were not ready to form a coalition with Russia to fight Islamic State jihadists in Syria, after talks between President Vladimir Putin and French leader Francois Hollande.

"At the moment, unfortunately, our partners are not ready to work within the format of single coalition," Putin's spokesman Dmitry Peskov told reporters.

Turkish Prime Minister Ahmet Davutoglu on Friday sought to ease tensions with Moscow over the downing of a Russian warplane over Syria, and said the world must unite to defeat the Islamic State group.

Russia ordered sweeping retaliatory measures after Turkish fighter jets shot down the warplane on Tuesday, threatening ties between two rival players in the Syrian war and raising fears of a wider international conflict.

French President Francois Hollande and Russian leader Vladimir Putin agreed Thursday to coordinate strikes against Islamic State, but differences over Syria's future hampered efforts to bring Russia into a wider alliance to fight the jihadists.

Putin indicated France and Russia would swap data to help identify IS targets in Syria, as opposed to other groups opposed to the country's leader, Bashar Assad.

Russia's foreign ministry on Thursday urged nationals currently in Turkey to return home after tensions with Ankara soared over the downing of a Russian warplane.

"In connection with the existing terrorist threats on Turkish territory, we once again recommend that Russian citizens refrain from visiting Turkey, and recommend that Russians who are there for personal purposes return home," the foreign ministry said in a statement.

President Recep Tayyip Erdogan denied Thursday that Turkey bought any oil from the Islamic State group, insisting his country's fight against the jihadists was "undisputed".

"Shame on you. Those who claim we buy oil from Daesh (IS) are obliged to prove it. If not, you are a slanderer," Erdogan said, lashing out at Russian charges after the downing of a warplane on the Syrian border.

Syrian special forces launched an operation "behind enemy lines" to rescue the surviving crew member of a Russian warplane downed by Turkey, Syria's Al-Watan newspaper reported on Thursday.

"Eleven members of an elite unit of the air force intelligence service and a (Russian-language) translator, led by an officer, infiltrated 3.5 kilometers (two miles) behind enemy lines in the Al-Atira region on Tuesday and recovered the airman," the pro-government newspaper said.