Austria quarantined 12 people in close contact with a couple who were the country's first coronavirus cases, one of whom works as a hotel receptionist, the local government in the province of Tyrol said.

Shortly after the Italian couple tested positive for the virus on Tuesday, authorities sealed off the hotel where the woman worked in Innsbruck, the regional capital, locking in guests and staff while they tested 62 people for the virus.

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"The health condition of all 62 tested people is good," Tyrol's provincial government said in a statement on Wednesday, adding nine of those were put in a two-week quarantine for having been in close contact with the woman, as had three more from the couple's immediate social circle.

Broadcaster ORF said the nine people from the hotel were hotel staff who worked with the woman rather than guests.

A spokesman for the provincial government said the lockdown at the 108-room hotel opposite the city's main rail station had ended overnight.

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The infected man and woman, both 24, last week visited their home town near Bergamo in Lombardy, one of the two Italian regions at the centre of Europe's worst outbreak. They drove to Innsbruck on Friday, a hospital doctor treating them told a news conference on Tuesday.

While the woman works at the hotel in Innsbruck, a hub for Alpine tourism less than an hour's drive from the Italian border, her boyfriend had been visiting, officials said.

Neighbouring Italy has become a front line in the global outbreak of the virus, with 280 cases and 11 deaths, most in Lombardy and nearby Veneto.

On Sunday night, Austria shut down rail travel between Germany and Italy by denying entry to a train from Venice because of two suspected coronavirus cases among the passengers. The train was only let through when those two passengers' tests came back negative.

Chancellor Sebastian Kurz said the procedure would be repeated if others suspected of carrying the virus arrived at Austria's borders.

Tyrol is a vital transport corridor between Italy and Germany and includes the busy Brenner Pass. More than half the freight crossing the Alps passes through Austria.

The new coronavirus has killed about 2,700 people, most in China, and spread to 30 countries. The number of confirmed cases globally has risen above 80,000.

The Italian couple in Innsbruck no longer have a fever and are showing "few symptoms", the hospital doctor said.