Updated at 6:35 p.m. ET
President Obama on Friday acknowledged that U.S.-Russian relations have slowed since Russian President Vladimir Putin succeeded Dmitry Medvedev.
"I think there's always been some tension in the U.S.-Russian relationship after the fall of the Soviet Union," Mr. Obama said in a press conference at the White House.
"It is true that in my first four years in working with President Medvedev we made a lot of progress," he said, noting the new START Treaty and cooperation on Iran sanctions, among other things. "There's been a lot of good work that has been done and is going to continue to be done."
That said, he added, after Putin took office for the second time in 2012, "I think we saw more rhetoric on the Russian side that was anti-American, that played into some of the old stereotypes about the Cold War contest between the United States and Russia."
The president said he's encouraged Putin to "think forward as opposed to backwards on those issues with mixed success."
As a result of the current tension between the two nations, the president recentlyhe was slated to have with Putin in September on the sidelines of the G20 Summit in St. Petersburg, Russia. While Russia's recent decision to grant temporary asylum to former government contractor Edward Snowden was one reason the White House canceled the meeting, Mr. Obama said Friday the decision was not punitive.
"Our decision to not participate in the summit was not simply around Mr. Snowden," he said. "On a whole range of issues where we think we can make some progress, Russia has not moved."
The president insisted that he doesn't have a bad personal relationship with Putin and that their meetings are "candid, they're blunt. Oftentimes, they're constructive."
When the two leaders are photographed together, their body language may appear tense, he said, joking that Putin's "got that kind of slouch, looking like the bored kid in the back of the classroom." But he added, "the truth is is that when we're in conversations together, oftentimes it's very productive."
Still, Mr. Obama noted the emerging differences between the two nations over the conflict in Syria and human rights issues, such as gay rights. He said it is appropriate for the U.S. to pause and "reassess" its relationship with Russia while at the same time "recognizing that there are just going to be some differences and we're not going to be able to completely disguise them, and that's OK."
Mr. Obama reiterated that he doesn't agree with some lawmakers that the U.S. should boycott the 2014 Olympics in Russia over the two nations' differences.
"And one of the things I'm really looking forward to is maybe some gay and lesbian athletes bringing home the gold or silver or bronze," Mr. Obama said. "Nobody's more offended than me by some of the anti-gay and lesbian legislation that you've been seeing in Russia... And if Russia doesn't have gay or lesbian athletes, then, it'll probably make their team weaker."
The president's remarks came after Secretary of State John Kerry and Defense Secretary Chuck Hagel met in Washington with their Russian counterparts, Russian Foreign Minister Sergey Lavrov and Russian Defense Minister Sergei Shoigu.
After that meeting, Kerry said, "The relationship between the United States and Russia is, needless to say, a very important relationship, and it is marked by both shared interests and, at times, colliding and conflicting interests and, I think, we are all very clear-eyed about that."
Along with the United States' relationship with Russia, Mr. Obama on Friday acknowledged the continued threat from al Qaeda, which prompted the United States recently to close multiple embassies around the world. The president, however, said that the persistent threats from al Qaeda affiliates like al Qaeda in the Arabian Peninsula (AQAP) doesn't undercut his past assertions that the "core" of al Qaeda is in retreat.
"It's entirely consistent to say that this tightly organized and relatively centralized al Qaeda that attacked us on 9/11 has been broken apart and is very weak and does not have a lot of operational capacity, and to say we still have these regional organizations like AQAP that can pose a threat," he said. "It means that we've got to continue to be vigilant and go after known terrorists who are potentially carrying out plots or are going to strengthen their capacity over time. But this is an ongoing process. We are not going to completely eliminate terrorism."
The president also argued that his administration will bring to justice the people who carried out the terrorist attacks on the U.S. consulate in Benghazi, Libya -- even though they happened 11 months ago.
"Well, I also said that we'd get bin Laden. And I didn't get him in 11 months," the president said in response to questions about Benghazi. He also noted that federal prosecutors have filed criminal charges in the case, but he said the indictment is "sealed for a reason."
"But we are intent on capturing those who carried out this attack," he said. "And we're going to stay on it until we get them."
The president called the press conference on Friday to announce new steps the administration is taking to make government surveillance programs more transparent. He also took questions on, his eventual nomination of the next Federal Reserve chairman and immigration reform.