Austria is assembling a coronavirus taskforce to discuss whether to introduce border controls with Italy, where a fourth person has died.
About a dozen towns in Italy are in lockdown as authorities race to contain the biggest outbreak of coronavirus in Europe.
At least 152 people in Italy have been infected with COVID-19, the disease caused by the coronavirus, and there have been four deaths over the past 48 hours.
The latest victim was an 84-year-old man from Bergamo, according to Sky News Italia. He is the third death in the northern Lombardy region.
On Sunday evening, Austria refused entry to a train coming from Italy after the Italian State Railways informed Austrian train operator OBB that there were two people with fever symptoms on board.
“Tonight a train on its way from Venice to Munich was stopped at the Austrian border,” Austria’s interior ministry earlier confirmed.
The operator later confirmed to Sky News that all train traffic to and from Italy had been suspended – but the suspension was lifted within a few hours.
Concern has also been expressed by the French director of health Jerome Salomon, who said the situation was “worrying” and warned of further cases in France because of its proximity to Italy.
He told the France Info radio station that “anyone returning from Lombardy or Veneto with symptoms must be considered suspicious”, but said there were not yet any plans for border controls.
The two regions, both in the north of Italy, have ordered schools and universities to close for at least a week, while museums and cinemas have been shut and the last two days of Venice Carnival called off.
In developments elsewhere:
The first Italian fatality from the virus this weekend was a 78-year-old former construction company owner, who died in Padua in the Veneto region.
A second patient – a 77-year-old woman – died hours later in Lombardy, while another woman with the virus in the region died on Sunday.
The regional governor of Veneto, Luca Zaia, said he had dealt with several natural disasters during his career, including floods and earthquakes, but “this is the absolutely worst problem that Veneto has faced”.
Almost a dozen towns in Lombardy and Veneto, with a combined population of about 50,000 people, have effectively been placed under quarantine.
Residents have been urged to stay home and special permission is needed to enter or leave the designated areas.
Four Serie A football matches were postponed in the wake of the virus outbreak, while the Women’s Six Nations match between Italy and Scotland was cancelled.
The biggest jump in cases of COVID-19 was reported by authorities in Lombardy, which includes the country’s financial capital Milan, with 90 cases confirmed.
Authorities have expressed frustration they have not been able to track down the source of the virus spread in the north of Italy, possibly by a so-called superspreader.
It surfaced in the region last week when an Italian man in his late 30s in Codogno became critically ill.
“The health officials haven’t been yet able to pinpoint Patient Zero,” Angelo Borrelli, head of the Civil Protection Agency, told reporters in Rome.
At first, it was widely presumed that the man was infected by an Italian friend he dined with and who recently returned from his job, based in Shanghai.
When the friend tested negative for the virus, attention turned to several Chinese people who live in town and who frequent the same cafe visited by the stricken man.
But Lombardy governor Attilio Fontana told reporters all of those Chinese people had tested negative, too.
Following the developments in Italy, the European Commission has announced a €232m (£195m) aid package to help member states and the global effort to tackle the outbreak.
While most cases and fatalities are still being reported in China, other countries have continued to step up their precautionary measures – with about 380 foreigners having been quarantined in North Korea.
Diplomatic staff are not being allowed out of their compounds in the reclusive state or to leave the country – including the British embassy, Sky News understands.
And another 70 more cases have been confirmed in South Korea, bringing the total number there to 833.
More than 2,470 people have been killed by the coronavirus outbreak, most of them in China.
There have been more than 79,000 suspected and confirmed cases of COVID-19 worldwide.