The website of Hungary's Olympic Committee quoted Chairman Zsolt Borkai as saying a "threatening message" was being taken "seriously" and had been forwarded to the International Olympic Committee, ABC News reported Wednesday.
NBC news reported the IOC said the threat appeared to be "a random message from a member of the public" and did not appear to be credible.
The U.S. Olympic team is one of at least six teams that received warnings, NBC said.
Italy's Olympic Committee reported Wednesday it had received a similar threat, the Italian news agency ANSA reported. The committee said it was "serene" about concerns for the safety of Italian athletes and expressed "trust" in the Games' security measures.
The Olympic committees of Slovenia and Austria also reported terroristic threats to its athletes. A Slovenian Olympic official said an email titled "The very dangerous terrorist threat to Slovenian athletes in Sochi, Russia" had been received. He said the message was a false alarm.
The IOC downplayed the email, saying it "contains no threat and appears to be a random message from a member of the public." The committee said it had determined the email "did not contain a threat" but was "an 'opinion' about security around the games from one individual."
All the threats were reportedly made in Russian and English.
Russia has instituted security measures around Sochi it has dubbed the "ring of steel." Tens of thousands of troops have been stationed in the area, a massive surveillance program has been instituted and anti-aircraft missiles have been installed.
Three possible female suicide bombers are being sought by Russian police. One of the women, Ruzanna Ibragimova, 22, is believed to have already entered Sochi.