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Despite the assurances, the letters to committees in Italy, Hungary, Germany, Slovenia and Slovakia briefly caused alarm and underlined nervousness about security at the $50 billion event on which Russian President Vladimir Putin's legacy may depend.
The U.S. Olympic Committee later confirmed that it also received a letter by email.
Suicide bombers killed at least 34 people in a city in southern Russia last month, Islamist militants have threatened to attack the Winter Games and security forces are hunting a woman suspected of planning a suicide bombing and of being in Sochi already.
"I am very pleased to inform everyone that both the IOC and the Sochi organising committee ... declared after the analysis of the letter that this threat is not real," Zsigmond Nagy, director of international relations at the Hungarian Olympic Committee, told Reuters.
He said "this person has been sending all kinds of messages to many members of the Olympic family."
The letter, he said, threatened Hungarian nationals, competitors and officials, saying that "persons attending the Olympic Games might be blown up."
Nagy also quoted IOC officials saying the letters had been sent by someone living outside Russia who had carried out such hoaxes before, but did not identify the person. He said there was "nothing to worry about."
In addition to Hungary and the United States, Italy, Germany, Slovakia and Slovenia said their national committees also had received threats and all had passed them to police.
"We have received the email in question and we have forwarded the message to the appropriate authorities," U.S. Olympic Committee CEO Scott Blackmun told Reuters. "The safety and security of Team USA is our top priority."
The committee is working with the U.S. State Department, local organizers and law enforcement to protect the U.S. delegation and other Americans traveling to Sochi, he said.
Earlier on Wednesday, U.S. lawmaker Michael McCaul, chairman of the House of Representatives' Homeland Security Committee who recently toured Sochi, told CNN he had not heard of any threats against the U.S. Olympic team.
"Not to the U.S. Olympic team," he said from Moscow. "There are threats. I can't go specifically into these, but not to the American team."
The IOC, which is based in Switzerland, moved quickly to ease concern after the first of the letters was received in Budapest. It said it took security very seriously and passed on any credible information to the relevant security services.
"However, in this case it seems like the email sent to the Hungarian Olympic Committee contains no threat and appears to be a random message from a member of the public," it said.
RUSSIA ON HIGH ALERT
The IOC has said it is confident that the games, opening in Sochi on the shores of the Black Sea on Feb. 7, will be safe, and Putin has put about 37,000 security personnel on combat alert in the Black Sea resort and increased security nationwide.
Russia also has been discussing its security operation with the United States, and Putin, who has played a big role in winning and organising the games, spoke about security at Sochi with U.S. President Barack Obama by telephone on Tuesday.
Even so, Moscow has failed to dampen concern that it will be able to guarantee visitors' and competitors' safety, despite the most elaborate security preparations for an Olympics.
A militant leader, Doku Umarov, has called for insurgents fighting for an Islamist state in Russia's North Caucasus to attack Sochi - which lies on the western edge of the Caucasus mountains where the insurgency is focused.
Security concerns were heightened by the suicide bombings last month in Volgograd, a southern Russian city that serves as a gateway to the North Caucasus, and by a video in which the Islamist militant group which claimed responsibility for the attacks threatened more violence.
In Sochi, which plans to host hundreds of thousands of visitors during the games, security forces are searching for a woman called Ruzanna Ibragimova, 23, who they suspect may be planning a suicide attack.
She may have arrived in the Olympic host city on Jan. 11-12, a letter seen by Reuters said.
"(She) may be used as a terrorist-suicide bomber by (insurgency) leaders to organise terrorist acts during preparations for and during the 2014 Winter Olympics," read the letter, asking police to look immediately into the matter.
The letter from Russia's Federal Security Services to local police said she was the widow of a slain Islamist militant and is believed to have recently left her home in Dagestan, in the turbulent, mainly Muslim North Caucasus.
Photographs of Ibragimova show a woman in a hijab, wearing a long dress.
Some Russian media say Russian forces may also be looking for other would-be suicide bombers known as "Black Widows", but the reports have not been confirmed.