The New York Post reported on June 14 that Kraft had told a US audience that he had once met Putin in 2005 and showed him the USD 25,000 ring that team players and owners are awarded for winning the US football league final.
Kraft said that Putin took the ring in his hands and then slipped it in his pocket after first joking that "I could kill someone with this ring."
Putin's official spokesman dismissed the story last weekend by saying that he was personally witness to Kraft giving the Russian leader the ring as a present.
Putin himself was unexpectedly asked about the incident for the first time by the US moderator of his appearance at a Saint Petersburg forum with German Chancellor Angela Merkel.
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"You know, I do not remember either Mr. Kraft or the ring," Putin said.
"We will ask our enterprises to craft a really good, noticeable thing, so it is clear that it is expensive, made of a good metal, with a rock, so that this jewel is passed on from generation to generation in the team whose interests Mr. Kraft represents.
"I think that this would be the most intelligent... solution to such a difficult international problem," Putin said with a hint of a smile.
Kraft said at the US event that he had even told the White House he would love to get the 4.94-carat ring back from Putin because it meant so much to him and his team.