“Change your heading south immediately,” a voice apparently says in English. Turkey said it had tried to rescue the SU-24 bomber’s two pilots.
One of them was killed by gunfire as he parachuted from the burning plane.
The other pilot was rescued. He denied claims the jet had violated Turkish airspace and warnings had been given.
The plane crashed into a mountainside on Syrian soil after being hit by a missile from a Turkish F-16 fighter jet on Tuesday.
Tensions have escalated between the two countries over the incident, with Russian President Vladimir Putin describing it as a “stab in the back” and warning of “serious consequences”.
Moscow later broke off military contacts with Ankara and said it would deploy its most advanced anti-aircraft missile system in Syria to destroy any target that may threaten its warplanes.
It also said fighter jets would now escort its bombers during air strikes over Syria. On Thursday, Russia said it would impose stricter controls on food and agriculture imports from Turkey.
The US, the EU and the UN have all appealed for calm.
French President Francois Hollande is travelling to Moscow on Thursday to shore up support for action against the so-called Islamic State (IS) group, which killed 130 people in attacks in Paris earlier this month.
The Turkish military said it had given 10 warnings to the Russian plane before it was shot down in Turkish airspace.Media caption Capt Murakhtin spoke to Russian media outlets, who did not show his face
Turkish officials also say they did not know the jet was Russian until they had shot it down.
On Wednesday, the Turkish military also put out a statement saying it had been in touch with Russian military attaches to explain the rules of engagement that led to the incident and that it had tried to rescue the pilots.
Turkey said it was ready for “all kinds of co-operation” with Moscow over the incident.
The surviving Russian pilot said on Wednesday no warning had been given by Turkey.
Capt Konstantin Murakhtin also stressed there was “no way” the jet could have violated Turkish airspace, as Ankara said it did.
He knew the region “very well”, he said, and the jet had not been in Turkish airspace “even for a second”.Media captionThe BBC’s Jonathan Marcus examines the increasingly risky air war over Syria
Russia said the pilot was rescued from rebel-held territory in north-eastern Syria in a 12-hour operation involving Russian and Syrian special forces.
A Russian marine was killed and a helicopter destroyed by rebels during the operation.
Syrian rebels released a video apparently showing the dead body of the second pilot, who was identified by Russia as Lt Col Oleg Peshkov.
Capt Murakhtin was speaking from the Hmeymim airbase, where Russia’s aircraft are based.
Russia has been carrying out air strikes against opponents of President Bashar al-Assad since late September.Media caption Protesters threw eggs and stones at the Turkish embassy in Moscow
Turkish President Recep Tayyip Erdogan has defended the action by the country’s military, saying “everyone must respect the right of Turkey to protect its borders”.
He said he did not want to escalate tensions further.
Turkey is a member of Nato. The alliance has backed Turkey’s version of events, although it, too, is calling for “diplomacy and de-escalation” to resolve the situation.
Russia and Turkey have found themselves on opposing sides in Syria’s conflict, with Russia supporting President Assad, while Turkey is a staunch critic.
Turkey is part of the US-led coalition against Islamic State.