The singer previously fell victim to pranksters who impersonated the Russian leader on the phone.
But Kremlin spokesman Dmitry Peskov told Russian media that Mr Putin had this time called the singer and asked him not to be offended by the hoax.
Mr Putin said on Thursday he was ready to meet Sir Elton - when their schedules allowed it - and discuss "any issues of interest" to the British star, Mr Peskov said.
`Prejudiced`
Russia has faced international criticism for its laws on homosexuality, including a 2013 bill prosecuting people for providing information about homosexuality to people under 18.
A report by Human Rights Watch last year said Russia was failing to prevent and prosecute homophobic violence amid a rise in attacks against minorities.
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Speaking to the BBC earlier in September, Sir Elton said Mr Putin`s attitude to gay people was "isolating and prejudiced" and "ridiculous".
He said he would like to speak to the president, although "he may laugh behind my back... and call me an absolute idiot".
Later a message on the musician`s Instagram account thanked Mr Putin for "reaching out" in a phone conversation.
But Kremlin spokesman Dmitry Peskov said reports of a conversation were "not true" and a recording of the hoax phone call was later aired on Russian TV.
Prankster Vladimir Krasnov admitted his involvement, telling the BBC and Russian newspaper Komsomolskaya Pravda that he made the call with his sidekick Alexei Stolyarov, known as "Lexus".
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