A pair of Russian comedians say they impersonated Russian President Vladimir Putin in a prank phone call to British singer Elton John, Russian media reported on Wednesday.

Vladimir Krasnov and Aleksei Stolyarov, known in Russia for targeting celebrities and politicians with their audacious stunts, say they called the British singer a day after he told journalists he would like to meet Putin to discuss gay rights.

"Yes, it was us," Krasnov was quoted as saying by Komsomolskaya Pravda newspaper. "I was 'Vladimir Putin'."

Kremlin spokesman Dmitry Peskov denied on Tuesday that Putin had made the call and suggested it could have been a prank after Elton John posted a photo of the Russian president on Instagram thanking him for the conversation.

"Thank-you to President Vladimir Putin for reaching out and speaking via telephone with me today. I look to forward to meeting with you face-to-face to discuss LGBT equality in Russia," the gay singer and campaigner wrote on Instagram.

Russia has been criticised by the West and human rights activists for its treatment of gay people and the Rocket Man singer has campaigned publicly against a 2013 law banning the dissemination of "gay propaganda" among young people.

Through a Russian interpreter, John is heard on the 11-minute call discussing a visit to Moscow with a man he believed was Putin.

"Tell him I am extremely honoured that he is calling me. It is a great privilege to be able to speak to one of the most influential people in the whole world. It's amazing," John says on the call, the tape of which was released to Reuters.

John agreed to travel to Moscow for a Gay Pride event, and said he hoped to have a "wonderful discussion" with Putin.

He concluded the call saying, "Tell him he has made my day, okay...it's a very wonderful moment in my life."

John's representatives did not immediately return calls for comment on Wednesday after it was revealed that he had been the target of a prank.