He declined to drink urine but Barack Obama did make tea from glacier water and munch on a bloody salmon previously chewed by a bear in his wilderness bromance with Bear Grylls.

The US president trekked through a remote part of Alaska to promote action on climate change – and show a more human side – in a special episode of the British adventurer’s reality show, Running Wild With Bear Grylls.

The hour-long programme, which aired on NBC on Thursday, showed the duo bonding as they hiked on Exit glacier in the Kenai mountains, bantering over fatherhood and the environment – as well as flatulence and bellybutton fluff.

“I’m skinny but tougher than I look,” said Obama, after the former soldier complimented his physical fitness. It was a moment to make Sarah Palin howl.

The president drank tea made from catkins and melting glacier water and munched on a ravaged salmon, which Grylls said had been discarded by a bear and still bore “bear breath”.

Grylls has persuaded previous celebrity guests to drink their own urine but the commander in chief demurred. “I suppose, in extremis, it’s something that I would do – if the alternative was death,” he said. “It’s not something I’d make a habit of. And I probably wouldn’t do it just for a TV show.”

It was the White House’s idea to pair the professorial president with a rugged survivalist as part of a strategy of unorthodox methods and stunts to project his agenda.

It was an Obama seldom seen on television: loose, personal, stripped of pomp, just a guy out hiking with another guy.

Of course, it was also an illusion. According to Grylls’ dozens of staff, secret service agents and a food taster hovered just off-screen, along with snipers in the hills and a military helicopter overhead.

Perhaps to offset any comparisons with Russian President Vladimir Putin’s swaggering wilderness photo-ops, Obama made several references to the invisible chaperones, including when he fumbled using a borrowed smartphone to take a selfie with Grylls.

“I’m in what’s called the bubble and secret service makes sure that I’m always out of danger, which I very much appreciate but it can be a little confining,” he said, addressing the camera directly. “So to be with Bear in the woods: it doesn’t get any better than that.”

Both men cited the retreating glacier as evidence of the urgency in addressing climate change. “I’ve two daughters, and I don’t want grandkids too soon, but eventually I hope to have some,” said Obama. “And I want to make sure that this is there for them, not just us.”

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He said action on climate change was vital to his presidency. “I think it will have a more significant impact on the lives of future generations as just about anything. And we’re still a long way from getting it right but it’s something that, working together, I think we can make a difference on.”

The show aired at a delicate time for the president, who is riding high on the climate deal agreed in Paris last week but defensive over Republican claims that he is weak on Islamist terrorism. On Friday he is due to visit the relatives of victims of this month’s San Bernardino massacre.

Obama played the straight man, noting Grylls’s reputation for extreme cuisine. “Bear’s a mediocre cook, but the fact that we ate something recognisable was encouraging. Now, the fact that he told me this was a leftover fish from a bear, I don’t know if that was necessary. He could have just left that out.”

The Briton commended the president on nimbly starting a fire, obviating need to use bellybutton fluff as kindling. He also recommended the catkins tea as a remedy for flatulence. “It’s not a problem I have but maybe you do,” Obama replied.

When Grylls warned that bears were especially dangerous when you surprised them “fornicating”, Obama joked that the same could be said for humans.

Clearly smitten, Grylls, an evangelical Christian, ended their outing with a riverside prayer calling on God to bless the president’s work. They hugged and went their separate ways.

“He said it was one of the best days of his presidency,” Grylls told reporters earlier this week, according to Reuters. “There were times along the route I had to pinch myself and think, ‘actually, this is the president of America’.”