WASHINGTON — President Barack Obama lauded Secretary of State Hillary Clinton as one of his closest advisers and said their shared vision for America’s role in the world persuaded his one-time rival — and potential successor — to be his top diplomat while he dealt with the shattered economy at home.

During a joint interview that aired Sunday evening, Obama and Clinton chuckled as they described their partnership and stoked speculation that Obama may prefer Clinton to succeed him in the White House after the 2016 elections.

Clinton is leaving Obama’s Cabinet soon, and speculation about the former first lady and senator from New York has only grown more intense after a heated appearance last week on Capitol Hill.

Both Obama and Clinton batted away questions about future campaigns, but the joint interview — the president’s first with anyone other than first lady Michelle Obama — was only likely to increase the fascination with Clinton’s future.

“The president and I care deeply about what’s going to happen for our country in the future,” Clinton said. “And I don’t think, you know, either he or I can make predictions about what’s going to happen tomorrow or the next year.”

Obama, who suggested the joint interview as Clinton prepared her exit from the State Department, lavished praise on his rival for the 2008 Democratic presidential nomination. He called her a friend and an extraordinary talent, and praised “her discipline, her stamina, her thoughtfulness, her ability to project.”

On the “60 Minutes” interview, he praised Clinton’s State Department for helping him sort out what the United States can — and cannot — accomplish.

“It has been a great collaboration over the last four years. I’m going to miss her. Wish she was sticking around. But she has logged in so many miles, I can’t begrudge her wanting to take it easy for a little bit,” Obama said.

His comments teetered on an endorsement of a 2016 presidential bid that is still an open question.

Clinton advisers say she has not made a decision about a run, while Democratic officials suggest Clinton would be an early favorite if she decided to mount another campaign.

Obama and Clinton laughed when asked about the political future.

“You guys in the press are incorrigible,” Obama said when pressed on another Clinton presidency. “I was literally inaugurated four days ago. And you’re talking about elections four years from now.”

The possibility of a presidential campaign for Vice President Joe Biden did not come up during the interview, taped Friday at the White House.