Islamist militants have threatened attacks during the Games in Sochi, which lies on the western edge of the mainly Muslim North Caucasus.
"It is correct that we got a letter, it was in the mailbox yesterday. We immediately contacted the federal criminal bureau, which is investigating," Peter Mennel, secretary general of the Austrian Olympic Committee, told the Austria Press Agency.
"I have already spoken to Ms Flock. Janine is sitting here with me on the plane. She is not concerned and is placing her trust in our protection," he was quoted as saying from a charter flight on the way to Sochi with several athletes.
He was confirming a report by the Krone paper that a letter, apparently from Russia, had arrived with the threat of abducting Schild - a former world champion and the all-time leader in World Cup slalom victories - and European champion Flock.
In a statement, the Olympic committee said it had received an anonymous letter targeting members of the team and had passed it on to the government. "At the moment we don't assume an acute threat," it added.
The Olympic Committees of the United States and several European countries received letters in Russian last month making a "terrorist threat" before the Games, but Olympic chiefs said they pose no danger.
Two Austrian special police officers are in Sochi to oversee the athletes if they leave the Olympic village, APA said.
Image: The Olympic rings at the Olympic Park in the Adler district of Sochi.
Photograph: Alexander Demianchuk/Reuters
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