LONDON — It was a story that seemed almost too good to be true. Russia’s president, Vladimir V. Putin, celebrated for his macho bravura, and the pop star Elton John, known for his elaborate costumes, ballads and gay activism, coming together in a phone conversation that the singer said had been initiated by the Kremlin.

“Thank-you to President Vladimir Putin for reaching out and speaking via telephone with me today,” Mr. John wrote in an Instagram post on Monday afternoon that went largely unnoticed for a day. “I look forward to meeting with you face-to-face to discuss LGBT equality in Russia.”

Once discovered, the Instagram post went viral. Many news organizations, including The New York Times, reported Mr. John’s account. The only problem is that, according to the Kremlin, the phone call never happened.