It's the most recent clash in a series of disputes between the two countries.
Russian President Vladimir Putin on Monday accused Turkey of shooting down the plane to protect secret oil trade with the terrorist group ISIS. He said the plane was actually going to attack ISIS targets in Syria.
Turkish President Recep Tayyip Erdogan said the plane violated Turkish airspace. He said he'll resign if Moscow can prove its claim.
"As soon as such a claim is proved, the nobility of our nation requires (me) to do this," Erdogan told reporters at the climate change summit in Paris on Monday.
But, he added, if the allegations are untrue, then Putin should resign.
"I am asking Mr. Putin, would you remain?"
So far, Putin has not responded to that question.
Moscow struck back economically
after the plane was shot down, banning the import of some Turkish goods, imposing restrictions on travel and planning to stop some Turkish companies doing business in Russia, CNNMoney reported.
Russia also took steps to restrict Russians from traveling to Turkey, which could hit the Turkish tourism industry hard.
The two countries hold widely different views about how to end the Syrian civil war and what should happen to Syria's leader.
Ankara's position is that Syrian President Bashar al-Assad has to go for the conflict to end -- a position also held by the United States.
Moscow backs Assad. In October Russian planes began airstrikes inside Syria.
Airspace has been a friction point in the past.
In early October, Turkey said it intercepted a Russian jet
that violated its airspace. The jet moved away when confronted by Turkish planes, Turkey said. Turkey then delivered a stern warning to the Russian ambassador.
Russia denied any aggressive intent, saying bad weather caused its jet to go off course.
Turkey: Putin's claim untrue
With his latest accusation, Putin is accusing Turkey of cooperating with ISIS.
"We have recently received additional reports that confirm that oil from ISIL-controlled territories is delivered to the territory of Turkey on an industrial scale," he said, according to TASS news agency
. (ISIS is also referred to as ISIL.)
"We have all grounds to suspect that the decision to down our plane was motivated by the intention to secure these routes of delivering oil to ports where it is loaded on tankers," he said.
Untrue, Erdogan said.
"It is obvious where we legally buy oil and natural gas from," Erdogan said, as reported by Turkey's Anadolu news agency
. "Everyone must know that we are not that disreputable to make such a deal with terrorist organizations."
Taking Turkey's side
In the bitter debate over where the Russian warplane was flying when it was shot down, the United States took Turkey's side Monday.
The available information indicates the warplane was in Turkish airspace, State Department spokeswoman Elizabeth Trudeau said.
Also Monday, the body of the Russian pilot, Lt. Col. Oleg Peshkov, was flown back to Russia.