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Caroline Kennedy, the newly minted U.S. ambassador to Japan who backed President Obama over Hillary Clinton in 2008, suggested to ABC News in a new interview that she would support Clinton if the former secretary of state ran for president again in 2016.

Kennedy told ABC's Jon Karl that she wants Clinton to run.

"I'm sure she's looking forward to being a grandmother," Kennedy said. "I know she's got to decide soon, so I hope so."

Asked whether she could see herself backing Clinton, Kennedy said: "Absolutely."

Kennedy made her high-profile endorsement in 2008 alongside another member of the fabled Kennedy family, the late Sen. Ted Kennedy (D-Mass.). It was seen as a major shift in that Democratic primary, which Clinton had been expected to win.