Despite fraught relations between the two countries after a Russian pilot was killed last week, the Turkey's PM demanded communication channels be opened up to stop similar incidents from occurring.
Ahmet Davutoğlu told a news conference: "Our call to Russia again is to open military communication channels to prevent similar incidents happening. Let's keep diplomatic channels open."
His call for dialogue comes after the Kremlin closed an emergency phone line with Ankara in anger at the attack, which Russia claims happened over Syrian airspace.
Turkey has refused to apologise for the strike, saying it has a duty to defend its territory.
But striking a more conciliatory tone today, Mr Davutoğlu said: "We must sit down and talk at the table instead of making unfounded allegation."
Vladimir Putin, who has signed a decree imposing economic sanctions on Turkey over the incident, said on Monday that Turkey shot down the Russian jet because it wanted to protect supplies of oil from ISIS militants.
Turkish President Tayyip Erdogan has called claims that Turkey buys oil from ISIS "slander" and told the Kremlin: "If you allege something you should prove it."
Speaking yesterday after talks between Mr Davutoğlu and Nato secretary general Jens Stoltenberg, the Turkish premier warned that conflicts in the skies above Syria would be difficult to prevent in the future unless Russia and the US-backed coalition worked together.
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