Vladimir Krasnov -- who goes under the nickname Vovan -- said he called up the pop star pretending to be Putin after the singer said he wanted to meet the Kremlin strongman to discuss gay rights.
"He was very happy and said that the call had made his day and that it was a miracle that it had taken place," Krasnov told AFP.
Krasnov -- whose previous victims have included Belarussian leader Alexander Lukashenko -- said he spoke in Russian while a fellow prankster translated his words into English pretending to be Putin's press spokesman and that the conversation would be broadcast on a Russian chat show later Wednesday.
A Kremlin spokesman, however, denied that Putin had made contact with the "Rocket Man" singer.
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The 68-year-old music star said in an interview over the weekend that he would like to discuss Russia's attitude to gay rights with Putin.
"I'd say, come on. Gay people are not the problem here," the singer told BBC television.
In 2013, Putin signed off on a hugely controversial law banning the promotion or display of homosexuality in front of minors.