"Vladimir Putin invited British specialists to take part in decoding flight data recorders of the downed Su-24," the Kremlin said after the phone talks with Cameron.
Russia has recovered the black box recording flight data from the fighter jet and Defence Minister Sergei Shoigu showed the orange-painted box to Putin during a Kremlin meeting on Tuesday evening.
Turkey shoots down Russian military plane on Syria border
Putin said at the Kremlin meeting that it should be analysed with the involvement of foreign experts to determine the plane's flight path and position, on which Moscow and Ankara furiously disagree.
Cameron, whose country last week launched its own bombing campaign in Syria, expressed condolences over the downing and the two leaders discussed cooperation, the Kremlin said in a statement.
Russia accuses Turkey's Erdogan over IS oil trade
"It has been noted that Russia and Britain have similar approaches regarding the threat from ISIL and other terrorist groups operating in the region," the Kremlin said, referring to the Islamic State (IS) group.
The two leaders also discussed ramping up cooperation "in this context", the statement said without providing further details.
Russia has been pushing for the creation of a broad anti-IS coalition since launching its controversial bombing campaign in Syria in September.
After the November 13 Paris attacks Putin hosted French President Francois Hollande in Moscow, with the two agreeing to increase cooperation on Syria and share intelligence.
Kremlin says Putin ‘fully mobilised’ to tackle threat from Turkey
The Kremlin however has lamented that global powers such as the United States, which has been bombing IS targets in Syria together with its allies for more than a year, are not ready to form a coalition with Russia.
Relations between Moscow and London have been tense for years.
Russia recently critised Britain for suggesting that a bomb caused the crash of a Russian passenger plane over Sinai in October before the investigation was completed.
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