The British Olympic Association (BOA) is one of a number of national federations to have received an email containing the terrorist threats, but the organisation insisted that the message "lacks credibility".
Federations from Italy, Germany, Hungary and Slovenia have also indicated they had received emails or letters with similar content, which were passed to the International Olympic Committee security advisers.
The threats follow the shooting dead of a senior Islamist militant in Russia's troubled North Caucasus as part of a security clampdown for the event at the Russian resort from February 7 to 23.
Last month, the southern city of Volgograd was targeted in twin suicide attacks. In the first, a woman blew herself up at a railway station killing 16 people. A bus attack later killed 18 people.
Chechen extremists have since posted a video on websites claiming responsibility and warning that Sochi 2014 will be next.
BOA's director of communications Darryl Seibel said: "We have received what appears to be the same email that many other federations have received and the IOC has responded to state very clearly that, in their view, there is nothing of substance to this.
"In addition we have had our own experts take a look at this and they have responded in exactly the same way by stating that this is nothing credible. Organisations like ours receive correspondence of every type and it is not uncommon to come across something like this, that lacks credibility.
"It is extremely important in matters such as this that everyone maintains a level head and a sensible perspective."
Mr Seibel said the threats would not alter the rigid security arrangements already in place to protect the Great Britain team.
Meanwhile, Scotland was hailed as "punching above its weight" as 18 of the 56 competitors in Team GB are Scots, with Eve Muirhead and David Murdoch's curling teams leading the way.
Elsewhere, after a move that sparked criticism of Russia ahead of the Games, singer Elton John spoke out against its ban on homosexual propaganda, saying the law gave legal cover to extremists.