It was not known who made the threats, in a letter to the Austrian national Olympic Committee, although Islamist militants have warned of attacks to undermine President Vladimir Putin's hopes of using the Games to show Russia is a safe, modern state.
Sources close to the Austrian Olympic team identified the competitors Alpine skier Bernadette Schild and skeleton racer Janine Flock, the current European champion. Austrian media had earlier said it was Schild's sister, former world champion Marlies, who had been threatened.
Specialists were checking whether the threat should be taken seriously. Threatening letters sent last month to delegations in several countries, including the United States, were deemed by the International Olympic Committee to pose no danger.
"We informed the minister of internal affairs and Austria's police... there is no actual threat at the moment," Peter Mennel, general secretary of Austria's Olympic Committee, told reporters at Sochi's Adler airport.
"We have two security people here and if the threat is confirmed we will give additional security to the athletes," he said after flying in with the Austrian team, including one of the competitors who has been threatened.
He declined to name them but said he had spoken to one of the pair by phone and the other in person. He said one of the two told him: "I'm not afraid and I know we're in good hands.
A spokesman for the Austrian Interior Ministry confirmed the national counter-terrorism agency had been brought in to look at the origin and content of the letter.
"We have taken all precautionary measures. The people affected have been informed and the Russian authorities are aware," he said.
No other national Olympic committee reported receiving such letters this week.
Putin has staked his political and personal prestige on the Sochi Games, intended to show how far Russia has come since the Soviet Union collapsed in 1991. A bombing, suicide attack or hostage crisis would seriously threaten those ambitions.
Doku Umarov, one of the leaders of an insurgency for an Islamist state in the North Caucasus, urged followers last year to attack Sochi, which lies on the Black Sea at the western edge of the mountains where the insurgency is focused.
Russia has responded by building a "ring of steel" around the Black Sea resort and has about 37,000 security personal on high alert in and around the city.
Security concerns grew after suicide bombers killed at least 34 people in the southern Russian city of Volgograd in late December, and police have been hunting four "Black Widows", women they fear may be planning more suicide bombings.
Russian and IOC officials say they are confident that the about 6,000 athletes and several hundred thousand spectators at the Games will be safe.
"Every big event nowadays is under threat," IOC President Thomas Bach said in Sochi on Monday. "We have to address this. The alternative would be to surrender to terrorists."
- Politics & Government
- Sports & Recreation
- President Vladimir Putin
- Bernadette Schild
- national Olympic committee