Right-wing politicians in France and Switzerland have called for borders with Italy to be closed or more closely monitored.
As Italy deals with a surge of confirmed cases of the COVID-19 virus, other European Union member states are considering what measures to take to prevent the disease from crossing the Alps.
Italian authorities confirmed on Monday that a fifth person had died on its soil from the novel coronavirus and that the number of cases had risen to more than 200.
The governments of Slovenia and Croatia, where no cases have been reported, convened emergency meetings on Monday. Zagreb has since announced that all travellers arriving from Italy would be monitored and that all scheduled school trips to Italy over the coming weeks would be cancelled.
The Croatian Foreign Affairs ministry also updated its travel advisory, advising its nationals to avoid visiting the northern Italian regions of Veneto and Lombardy because of the "risk of coronavirus infection".
Further east in Romania, authorities have announced that all Italian nationals from Italian regions where cases of COVID-19 have been confirmed will be quarantined for 14 days. The AP news agency reported however that people at the border are only required to fill a form.
To close or not to close the borders
In France, right-wing MP Eric Ciotti from the border region of the Alpes-Maritimes, has written to the government calling for controls at the border to be stepped up.
Marine Le Pen, the leader of the far-right Rassemblement National party, has echoed his call but such demands have been dismissed as "useless" by Jerome Salomon, the head of the General Directorate of Health.
"Every person who returns from Lombardy or Veneto with symptoms must be considered suspicious," Salomon said, however.
"What is important is to quickly identify each contagious person. This is why in the next few hours we will undoubtedly have cases, the number of people being examined must increase," he added.
The Swiss Federal Office of Public Health (OFSP) has not yet announced additional measures, stressing however that authorities are monitoring developments in Italy closely.
In the Canton of Ticino however, people presenting symptoms of respiratory infection are considered suspect and isolated. A coordination group was scheduled to meet on Monday to decide whether further measures are necessary in light of the situation in northern Italy.
The deputy leader of the national-conservative Lega dei Ticinesi party, Lorenzo Quadri, has called for the canton to close its border to the 70,000 frontier workers from Lombardy who come into the country every day.
In Austria, train traffic to and from Italy resumed on Monday following a four-hour-long interruption on Sunday evening.
The Mediterranean island-state of Malta has announced that all passengers arriving on the island would be checked with thermal scanners.
'Moderate to high'
The European Centre for Disease Control (ECDC) on Sunday increased its assessment about the risk of the occurrence of COVID-19 clusters similar to the ones in Italy, in other countries in the EU/EEA and the UK to moderate to high.
The EU Commission has also announced that it had allocated €230 million to the global fight against the disease.
Stella Kyriakides, the EU Commissioner for Health and Janez Lenarcic, the Commissioner for Crisis Management called for evidence-based measures, proportionate responses implemented "in collaboration with other states".
"The question of travel bans and border controls is the responsibility of the various countries," Lenarcic reiterated, stressing that no member states have so far called for a suspension of the Schengen area and that "they have coordinated well".
"But we can always improve and I am not only talking about cooperation between EU countries, but also outside the EU," he said.
Prime Minister Giuseppe Conte argued that Italy has the most confirmed cases in the EU because it has carried out the most tests, over 4,000.
Virologist Laria Capua told the RAI that the country is experiencing a "flu-like syndrome caused by coronavirus" which could last "until late spring or before summer".