With only days left until she steps down as America's top diplomat, Hillary Clinton left the door open Sunday to a possible future run in the 2016 presidential elections.

And, in a rare joint interview with CBS, she appeared to win the endorsement of none other than President Barack Obama, the man who beat her in the 2008 race to be the Democratic Party's nominee.

For months, 65-year-old Clinton has insisted that after more than two decades in the political spotlight she intends to step back into the shadows, catch up on some rest and enjoy some downtime for a change.

But with her popularity riding high -- at around 65 percent according to a Washington Post-ABC poll last week -- many believe she will bounce back to take another shot at being the nation's first woman president in 2016.

"I am still secretary of state. So I'm out of politics," Clinton told CBS television's "60 Minutes" carefully, leaving herself the option of reviving her career once she leaves government.

A woman who has devoted much of her life to public service, as first lady and as a New York senator, she stressed she still cared "deeply about what's going to happen for our country in the future."

Clinton said neither Obama nor "I can make predictions about what's going to happen tomorrow or the next year," in comments bound to rekindle speculation that she could be preparing a 2016 run.

"What we've tried to do over the last four years is get up every day, have a clear eyed view of what's going on in the world. And I'm really proud of where we are," she added.

Obama did nothing to dampen speculation, heaping praise on Clinton and saying he believed she "will go down as one of the finest secretaries of state we've had."

"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.

"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.

The joint sit-down interview, which was filmed at the White House, was apparently Obama's idea, and some observers saw it as an early endorsement should she choose to run for president in 2016.

Obama will have to stand down after serving the statutory maximum of two terms, but his endorsement is likely to give any candidate a big boost.

Often the vice president becomes the natural choice as the incumbent party's presidential nominee. It is not clear yet if Vice President Joe Biden will make a tilt for the White House, but he will be 73 years old come 2016.

Obama hailed Clinton for having been one of his "most important advisors," saying she had established "a standard in terms of professionalism and teamwork in our cabinet, in our foreign policy making."

Their relationship had evolved into a friendship, with "a sense of trust and being in the foxhole together," he said.

He told CBS he had asked Clinton from the start of her tenure in 2009 to go out and represent America abroad so he could focus on dealing with the economic crisis facing the nation.

But he dismissed criticism the United States had become reluctant to take a lead in the more complicated issues of the day, such as Syria, arguing the late Libyan dictator Moamer Kadhafi probably would not agree with that assessment.

"We do nobody a service when we leap before we look. Where we... take on things without having thought through all the consequences of it," Obama said.

"Our job is to, number one, look after America's security and national interest. But number two, find where are those opportunities -- where our intervention, our engagement can really make a difference."