"We think the greater danger, from a terrorist perspective, is in the potential for attacks to occur outside of the actual venues for the games themselves, in the area surrounding Sochi or outside of Sochi, in the region," said Matthew Olsen, director of the National Counter-terrorism Center.
Security at the Sochi winter games has been a major focus for Moscow as well as Washington, after two deadly suicide attacks in December in the southern city of Volgograd and a stream of threats from Islamist militants in the volatile northern Caucasus region.
"It's made its intent clear to seek to carry out attacks in the run-up to the games," Olsen said.
US intelligence services are monitoring "a number of specific threats of varying degrees of credibility," he said.
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But he added: "This is what we expected. It's what we saw in the run-up to prior Olympic games and prior events like these."
Asked about the extent of cooperation from Russian authorities after complaints from US officials, Olsen said Moscow was sharing information even though "there's always more we could do in that regard."
James Clapper, director of national intelligence, said cooperation had improved compared to three years ago and that the Russians "are more prone to cooperate when it's an external threat, less so with an internal threat."
The White House had expressed concern last month about Russia's reluctance to share details of various security threats to the games.