The two countries are releasing conflicting accounts of the incident, with the surviving pilot rejecting Turkish claims the plane was given ample warnings.
Turkey has released audio which, it says, recounts the moments before the plane was shot down.
The Russian two-man fighter jet was hit by missile fire from Turkish aircraft as it flew a mission along the Syrian-Turkish border.
The Russian air force has been bombing Syrian rebel targets in that area, but Turkey says the plane encroached on Turkish airspace and was warned repeatedly to change course.
Russian officials deny those claims, saying the plane was never over Turkey and was always in Syrian airspace.
Turkey maintains the jet had flown more than a kilometre and a half into Turkish airspace for 17 seconds.
It has now released what it says is the cockpit audio recording, in Turkish, warning the Russian jet to change course.
The United States military also says Turkish pilots warned the Russian jet 10 times but failed to get a response.
But one of the rescued Russian aviators from the fighter jet has told Russian media there was nothing.
Captain Konstantin Murakhtin says there was no warning before they opened fire.
"There were no warnings, not via the radio, not visually. There was no contact whatsoever. That's why we were keeping our combat course as usual. If they'd wanted to warn us, they could have shown themselves by heading on a parallel course. There was nothing, and the rocket hit our tail."
The pilot was killed after parachuting from the plane, and a marine who went to rescue the men was also killed.
Russia has spoken about taking retaliatory action.
It has since deployed an advanced missile-defence system to its air base in Syria and is threatening to cancel joint business contacts with Turkey.
Russian foreign minister Sergey Lavrov has also cancelled a planned visit to Istanbul in the wake of the incident.
And Russia is advising its citizens not to visit Turkey, due to what it calls a security threat.
But Mr Lavrov says Russia does not want a military escalation as a result of the downing of the plane.
"We're not intending to go to war with Turkey. We're not changing our opinion about the Turkish people. We're just assessing the actions of the current Turkish government."
Turkish president Recep Tayyip Erdogan also seems keen to calm tensions.
"Turkey does not have any intention to escalate the situation. What we are worried about is to defend our security and to defend the rights of our brothers in the north of Latakia, in the regions which are populated by Bayirbucak Turkmen. There is a wave of migration towards our borders, and we are trying to protect our kin, our brethren."
United Nations spokesman Ahmad Fawzi says the incident could complicate international efforts to battle the self-proclaimed Islamic State, or I-S, also know as ISIL, in Syria.
"All of us want to see an end to terror in that region and in our lives. And for that, nations have decided that they would deploy all necessary measures to do so."
In Australia, Federal Opposition foreign-affairs spokeswoman Tanya Plibersek has told the ABC both sides need to refocus on defeating IS.
"What we need to do, I think, over the coming days and weeks is refocus the attention of both Turkey and Russia on the common objective of defeating IS, or Daesh. We've now got more than 60 countries involved in a coalition to fight Daesh, and making sure, of course, that we have clear lines of communications between all of the countries involved, particularly those who are operating above Syrian airspace, is critical, and making sure that we have the common objective of protecting civilians and fighting Daesh, or IS. We need to be very clear about that."
Foreign Minister Julie Bishop says she believes the two sides will be able to put aside their differences.
"I hope that having referred it to the Security Council, both parties will now take the time to investigate this properly, deal with the varying versions of what went on, and then come together to attack the enemy in all of this, the enemy in Syria and Iraq, which is ISIL, Daesh, the terrorist organisation."
Share
