Seven more have been injured, one of them critically, the Interfax news agency cited a source as saying. Russia’s Emergencies Ministry confirmed 23 people had been on board the plane, the RIA news agency reported.
Some eyewitnesses have put the death toll at 19.
The plane was carrying a group of 21 parachute jumpers on board, the Emergencies Ministry said, according to the TASS news agency.
Eyewitnesses have suggested it crashed immediately after take-off.
A source said: "Four more people have been rescued by fire and rescue teams, work continues.
"Overall, seven people have been rescued."
If accurate, the information would contradict earlier reports by emergency services that 19 people had died.
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The source added: "This information has not been confirmed, access to the plane’s half-ruined fuselage is impeded."
The plane was a Let L-410 Turbolet, which is a twin-engine short-range transport aircraft.
One Russian broadcaster tweeted "eyewitness footage from the crash site of the L-410 aircraft in Tatarstan, adding: "The source reports 19 dead."
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A rescue team has been flown to the crash site on an Mi-8 helicopter.
The aircraft, which had been in service for 34 years, had been used to training paratroopers at Menzelinsky flying club.
Russian aviation safety standards have improved in recent years but accidents, especially involving ageing planes in far-flung regions, are not uncommon.
An ageing Antonov An-26 transport plane crashed in the Russian far east last month killing six people.
All 28 people on board an Antonov An-26 twin-engine turboprop died in a crash in Kamchatka in July.
(More to follow)