US President Barack Obama Friday heaped praise on outgoing Secretary of State Hillary Clinton in a rare joint interview set to renew speculation that she will run for president in 2016.

The joint sit-down interview with CBS television, which was filmed at the White House, was apparently Obama's idea.

"I just wanted to have a chance to publicly say thank you, because I think Hillary will go down as one of the finest secretaries of state we've had," Obama said in an excerpt shown on CBS ahead of Sunday's "60 Minutes" program.

"It has been a great collaboration over the last four years. I'm going to miss her," he added, saying he wished she was staying on.

Many people were surprised when Obama named Clinton to be his secretary of state, after the two fought a long and bitter battle for the Democratic Party's presidential nomination in the 2008 elections.

Clinton was just beaten by Obama in the historic race, which went down to the wire, and many observers believe she could well try again to become the nation's first woman president in the 2016 elections.

A public endorsement by the sitting president would give added weight to her candidacy -- although she is already riding high in the popularity stakes with an approval rating of around 65 percent.

"I want the country to appreciate just what an extraordinary role she's played during the course of my administration and a lot of the successes we've had internationally because of her hard work," Obama added.

Clinton, who is tapped to be replaced in the coming days by Senator John Kerry, acknowledged that it would have seemed "improbable" that she would have joined forces with Obama a few years ago.

But she said she had used her 2008 defeat as a useful lesson about the workings of democracy in her travels.

"I think it helps them understand. I say, look, in politics and in democracy, sometimes you win elections; sometimes you lose elections," she said.

"I worked very hard but I lost and then President Obama asked me to be secretary of state and I said yes and why did he ask me and why did I say yes? Because we both love our country."

Obama rarely sits down for joint interviews with anyone other than his wife, Michelle. An exception was one he gave with former French president Nicolas Sarkozy in November 2011 on the sidelines of a G20 summit in Cannes.