Eye-Opening Women: Caroline Kennedy

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(CBS News) Caroline Kennedy -- rumored to be the next American ambassador to Japan -- has been honoring the memory of her father, John F. Kennedy, by recognizing courage in public service since 1990. Kennedy serves as the president of the JFK Library Foundation and is a member of the John F. Kennedy Profile in Courage Award selection committee. She joined "CBS This Morning" Friday as part of "Eye-Opening Women," a Women's History Month series.

Kennedy called the selection process "really inspiring" and announced former Rep. Gabrielle Giffords as the 2013 recipient of the Profile in Courage Award.

"Everybody knows of her tremendous, incredible courage, but the fact that she went through this obviously horrendous tragedy and has recommitted herself to the political process ... is something that is really inspiring," Kennedy said. "For anybody in public life ... it is tough these days."

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Kennedy said Giffords was surprised to get news of the award from Kennedy herself, who called their conversation "wonderful" and "heartwarming."

She added that Giffords is "one of the most courageous people any of us have ever seen," saying "this award has really taught me that there are people who are courageous at all levels of government."

Turning to personal politics, Kennedy, who was an early supporter of President Obama, said she would support former Secretary of State Hillary Clinton as a presidential candidate in 2016 and denied any presidential aspirations of her own.

Speaking to the rumored ambassadorship, Kennedy explained that she remains "an incredibly strong supporter of the president."

"I think service is important, and I'd love to serve in any way," she said before adding, "No one has asked me [about the ambassadorship]."

Despite her insistence that she has yet to discuss an ambassador's post with the White House, Kennedy left a hint in the "CBS This Morning" studio, leaving a goodbye note that reads, "Come to Tokyo!"