US president Barack Obama says while Russian president Vladimir Putin may seek to look like the tough guy in their joint appearances, the two leaders have a pragmatic and respectful relationship.

"I wouldn't call it icy," Mr Obama said in an interview with NBC host Bob Costas, taped on Thursday as part of coverage of the Winter Olympics in Sochi.

"He does have a public style where he likes to sit back and look a little bored during the course of joint interviews.

"My sense is that's part of his shtick back home politically as wanting to look like the tough guy."

Mr Obama says US politicians have a different style.

"We tend to smile once in a while," he said in the interview set to air on Friday (local time).

Mr Obama cancelled a visit to Moscow to visit Mr Putin last year after Russia granted asylum to Edward Snowden, the former spy contractor whose leaks about US surveillance operations rocked US relations with allies and hurt Mr Obama's popularity at home.

The leaders have also disagreed over how to respond to Syria's civil war.

In a joint appearance after discussing Syria at a meeting in June, Mr Obama and Mr Putin both looked like they would rather have been somewhere else.

Barack Obama says there's a surprising amount of humour when he meets Vladimir Putin. ( AFP Photo: Pablo Martinez Monsivais )

On Thursday, a recording of a private conversation between US diplomats discussing protests in Ukraine was posted on YouTube, embarrassing the United States.

"I would say that since the video was first noted and tweeted out by the Russian government, I think it says something about Russia's role," White House spokesman Jay Carney told reporters.

But Mr Obama said the two leaders focus on issues of "mutual concern" where they can work together.

"The truth of the matter is that when we are in meetings there are a lot of exchanges, there's a surprising amount of humour, and a lot of give and take," he said.

"He's always treated me with the utmost respect."

Mr Obama said US and Russian law enforcement, military and intelligence officials have been in "constant communications" to ensure safety at the Sochi Olympics.

"I think the Russians have an enormous stake, obviously, in preventing any kind of terrorist act or violence at these venues. They have put a lot of resources into it," he said.

Reuters