Putin was reacting Sunday through a spokesman to a New York Post story quoting remarks made by Kraft at an awards gala at the Waldorf-Astoria hotel last Thursday.
"I took out the ring and showed it to (Putin). And he put it on and he goes, 'I can kill someone with this ring,'" Kraft said, as quoted by the Post. "I put my hand out and he put it in his pocket, and three KGB guys got around him and walked out."
The diamond-encrusted Super Bowl ring worth about $25,000 changed hands while Kraft was visiting St. Petersburg, Russia, in 2005 with an American business delegation that met Putin. At the time, Kraft had said he gave the ring to Putin as a gift.
But the Post story quoted Kraft as saying at Carnegie Hall's Medal of Excellence gala that he had an "emotional tie to the ring" and wanted it back, but the White House intervened and said it would be in the interest of U.S.-Russian relations to claim it was a gift.
Putin arrived in London on Sunday to meet with British Prime Minister David Cameron, and Putin's spokesman, Dmitry Peskov, was asked about the Post story.
"Back in 2005 I stood behind the president's back and I saw how that ring was presented to him. All that talk about some kind of pressure that was exerted on him (Kraft) should be the subject of a detailed talk with psychoanalysts, I think," Peskov told The Associated Press.
"At the same time, I am aware that this gentleman (Kraft) is feeling such a horrible pain about the 2005 loss," Peskov said. "The president will be ready to send him another ring as a gift, which he (Putin) can buy with his own money."
Stacey James, a spokesperson for the Kraft Group, the holding company for Kraft's business ventures, including the Patriots, said Sunday that the Post article shouldn't be taken too seriously.
"It's a humorous, anecdotal story that Robert retells for laughs," James said in a statement. "He loves that his ring is at the Kremlin, and, as he stated back in 2005, he continues to have great respect for Russia and the leadership of President Putin. In particular, he credits President Putin for modernizing the Russian economy. "
The statement said "an added benefit from the attention this story gathered eight years ago was the creation of some Patriots fan clubs in Russia."
The Super Bowl ring is on display in the Kremlin library along with other gifts to the Russian leader, according to Peskov.
Kraft can take some consolation because he has two other Super Bowl rings given to him for his team's other NFL championships.
Associated Press writer Thomas Wagner in London and Associated Press sports writer Howard Ulman in Boston contributed to this report.