Diack said Russia gave 1.5 million euros (USD 1.6 million) to "associations and spheres of influence" in his native Senegal ahead of the vote in a bid to help prevent the re-election of Abdoulaye Wade, a source told AFP, confirming a report in Le Monde.
The payments were allegedly made via Valentin Balakhnishev, former president of the Russian Athletics Federation and ex-treasurer of the International Association of Athletics Federations (IAAF).
"It was necessary at the time to win the 'battle of Dakar' -- that is, change those who were in power in my country Senegal," Diack said, according to taped legal interviews cited by Le Monde.
"So, I needed finance... Mr Balaknishev was part of (Russian leader Vladimir) Putin's team and at the time there were these problems with the suspension of Russian athletes, several months before the world championships in Russia.
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"We agreed with each other; Russia paid up."
Approached by AFP, Diack's lawyer Alexandre Varaut denied there was any link between the payments and his attitude towards doping in Russia.
"This type of business is not in our interest or in our power. We cannot interfere in Senegal's interior affairs."
The Senegalese government also denied that Russia had meddled in the election to help incumbent president Sall.
"Lamine Diack, and even less so Russia, did not finance the campaign... Either directly or indirectly," presidential communications minister Hamidou Kasse told AFP.
"The campaign of President Macky Sall was financed by Macky Sall himself and through the commitment of activists."