Austrian Chancellor Sebastian Kurz has announced major restrictions on movement in public places, banning gatherings of more than five people and urging people to self-isolate.

The restrictions on public movement and gatherings came into force on Monday, while restaurants were ordered closed from Tuesday, when new restrictions on entering the country will also take effect, a government spokesman said.

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"Austrians are being summoned to isolate themselves," Kurz's office said in a statement. "That means only making social contact with the people with whom they live."

People should only leave home for work that cannot not be postponed, to buy necessary food supplies and to help others, it said.

Gatherings of more than five people will be allowed only for activities serving to fight the coronavirus outbreak, the chancellor's office added.

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People who feel they need to get outdoors "may do so, but only alone or with people living in the same apartment", Kurz told Austrian news service APA.

Police would be stationed at playgrounds and outdoors, and would ask large groups to disband, he added.

The country has had at least 800 cases, according to its health ministry.

The western region of Tyrol, home to the popular ski resorts where Austria's first cases were reported and where at least 245 cases had been confirmed, announced a total lockdown on Sunday.

The region has found itself in "the most difficult situation we've ever faced in the post-War years", according to the governor.

Austria also expanded the list of countries from which it restricts entry, adding the UK, the Netherlands, Russia and Ukraine. It said people travelling from countries on the list could enter only if they undertook two weeks of home quarantine after entering or had a current health certificate.

In an interview on Sunday evening, Kurz said the government intended to bring overall air traffic to a halt but was currently maintaining minimal flight connections in order to bring Austrians abroad back home.

"There are many Austrians abroad we are currently bringing home, but once that is completed, flight connections to any place with a risk will be completely stopped," he told Austrian broadcaster ORF2.

"The airport is already down to 20 percent operation ... Whoever is abroad and wants to come to Austria should urgently make themselves on their way, or contact the foreign ministry to be brought back home."

Austria has already closed its borders to most arrivals from neighbouring Switzerland and Italy because of the coronavirus outbreaks there. It has previously announced other measures, such as shutting schools and most shops - other than those selling food and medicine - from Monday.

The government said on Saturday it was making four billion euros ($4.4bn) immediately available to deal with the economic fallout from the pandemic.