WASHINGTON (REUTERS) - One of the most prominent women in the Democratic Party on Sunday encouraged outgoing Secretary of State Hillary Clinton to mount a White House run in 2016 to try to become the first woman president.

"I am a fan," California Senator Dianne Feinstein said on CNN's State Of The Union programme. "I would love it if she would run."

Ms Feinstein was asked whether President Barack Obama's decision to have a joint interview on the CBS show 60 Minutes - airing on Sunday - indicated the president's preference for his successor.

"Well, I'm not as concerned with that as I am with what Secretary Clinton is thinking about 2016," Ms Feinstein said. "I think she's accomplished an incredible record. I think she has really unbridled popularity. She has a total knowledge of all of the issues. She has served in the Senate. She has been first lady."

Mr Obama was sworn in for a second four-year term last week but speculation already has begun on who will run in 2016, with Vice-President Joe Biden's name also frequently mentioned among Democrats.

Mrs Clinton, 65, is stepping down as the top United States (US) diplomat after four years as Mr Obama's secretary of state. She ran for the 2008 Democratic presidential nomination but was edged out by Mr Obama, who became the first black president.

Mrs Clinton has played down any chances she will run again, commenting in December: "I've said I really don't believe that that's something I will do again. I am so grateful I had the experience of doing it before".