In something of a parting gift, President Obama is making abundantly clear his deep support and fondness for outgoing Secretary of State Hillary Clinton, who is leaving wide open a possible presidential run in 2016.

Sitting together for their first joint interview, you could almost forget that they once politically bludgeoned each other in the 2008 Democratic primary.

"I'm going to miss her," Obama told CBS News' Steve Croft on "60 Minutes." "Wish she was sticking around."

"A few years ago it would have been seen as improbable," Clinton admitted, before explaining that she ultimately agreed to take the position as secretary of state "because we both love our country."

"I'll tell you what I finally thought. You know, if the roles had been reversed, and I had ended up winning, I would have desperately wanted him to be in my cabinet," Clinton said.

Sitting casually next to each other, laughing and smiling, the president and Clinton praised one another effusively.

"I consider her a strong friend," Obama said, while Clinton described their relationship as "warm" and "close."

(CBS, File/AP Photo)

Obama said he proposed the joint interview because he wanted to publicly say "thank you" to Clinton for all of her hard work. For those eagerly looking for hints of Clinton's future ambitions, however, the interview certainly felt like a political endorsement.

Clinton notably offered no outright denial, when asked about her plans for 2016.

"Obviously the president and I care deeply about what's going to happen for our country in the future and I don't think either he or I can make predictions about what's going to happen tomorrow or the next year," she said.

"I am still secretary of state and forbidden from even hearing these questions," Clinton joked when asked about her future.

The president brushed off the question.

"You guys are incorrigible," he told Croft of the press. "I was inaugurated four days ago and you're talking about elections four years from now."

Clinton declared herself in good health, following her concussion last December that led to a blood clot.

"I still have some lingering effects from falling on my head and having the blood clot," she said, still wearing her glasses. "But the doctors tell me that will all recede. And so, thankfully, I'm looking forward to being at full speed."