President Barack Obama said on Friday it was appropriate for the US to pause and reassess its relationship with Russia, in the face of anti-America rhetoric and "backwards" thinking from President Vladimir Putin. Addressing the downturn in relations between Washington and Moscow, Obama noted that there were several issues of concern, not just the recent extradition spat over NSA whistleblower Edward Snowden.

"There are a number of emerging differences we have seen in recent months around Syria, around human rights," he said.

Obama's comments came as leading government figures from both sides met in Washington to discuss a series of issues. The so-called 2+2 meeting – between US secretary of state John Kerry, defence secretary Chuck Hagel and their Russian counterparts, Sergei Lavrov and Sergei Shoigu – took place after days of recriminations over Moscow's decision to grant Snowden asylum.

Earlier this week, Obama announced the cancellation of a summit in Moscow next month. That meeting, between two leaders who have had an uneasy relationship in the past, had been expected to be a chance for both sides to work on resetting diplomatic ties. Instead, the cancellation of talks has merely underlined the distance between the former Cold War foes.

Emerging from the top diplomatic meetings on Friday, Washington and Moscow officals pointed towards areas of cooperation. "Edward Snowden did not overshadow our discussions," Lavrov told reporters, adding that the issue did not affect "mainstream" US-Russian relations.

Kerry added that the meeting was important "above and beyond the collisions and the moments of disagreement".

Afterwards, Washington officials said that the talks had been "positive and constructive throughout". But they added that the issue of Snowdon's asylum had come up and that the US delegation had reiterated its displeasure.

In a near hour-long press conference at the White House, Obama was more stark in his assessment of current US-Russian relations.

"Frankly, on a whole range of issues where we think we can make some progress, Russia has not moved," he said. "I've encouraged Mr Putin to think forward rather than backwards on those issues with mixed success."

Obama went on to note that since Putin returned as president of Russia, there had been an upturn in anti-American rhetoric. The president added that he did not have a "bad personal relationship" with Putin, despite the body language sometimes employed by Putin when the pair meet. "He has that kinda slouch, like a bored kid at the back of the classroom," Obama noted.

Russian foreign minister Sergei Lavrov talks with US secretary of state John Kerry. Photograph: Win Mcnamee/Getty Images

Aside from Snowden and the ongoing distance between the two countries on the issue of Syria, the White House has also faced pressure over the forthcoming winter Olympics. The Games, which are due to be held in the Russian city of Sochi, have been overshadowed by a row over recent anti-gay and lesbian laws passed in Moscow. Some equal rights activists have called on the US to pull its athletes from the games.

"I do not think it is appropriate to boycott the Olympics," Obama said, while adding that "nobody is more offended than me by some of the anti-gay and lesbian legislation". He expressed a hope that gay American athletes would bring home gold medals.