European nations are examining extending the lockdowns put in place to try to stem the coronavirus outbreak.
A lockdown imposed on 12 March in Italy, where the number of deaths may soon overtake China, will now extend beyond the original 25 March end date.
France said its 15-day lockdown might also be extended, with European leaders reluctant to give any deadline for an end to crisis measures.
There have been 207,000 cases worldwide with more than 8,600 deaths.
The European Central Bank (ECB) has launched an emergency €750bn ($820bn; £700bn) package to ease the impact of the pandemic, with boss Christine Lagarde tweeting "there are no limits" to its commitment to the euro.
Europe's markets stabilised on opening, moving into positive territory, although Asian markets remained volatile with the Nikkei closing down 1%.
The EU has introduced strict border controls. Travellers from outside are being turned away from airports and borders after the 27-country bloc imposed a 30-day ban to halt the spread of coronavirus.
But EU leaders also agreed that internal borders that have been erected in recent days should come down.
Separately, the EU's Brexit negotiator, Michel Barnier, said he had tested positive for coronavirus.
He said on Twitter: "I am doing well and in good spirits."
It is unclear how the pandemic will affect Brexit talks. The latest round was delayed on Wednesday but the UK government said it would look at different ways to continue discussions.
What of the Italian and French lockdowns?
Italy shut down most businesses and banned public gatherings nationwide on 12 March.
But Prime Minister Giuseppe Conte said on Thursday: "The measures we have taken… must be extended beyond their original deadline."
He said the measures had meant "we have avoided the collapse of the system".
But he told Corriere della Sera that "we will not be able to return immediately to life as it was before" even when the measures ended.
On Wednesday, Italy reported that 475 more people had died in just one day. Any similar figure on Thursday would see it pass China's official death toll of 3,130, according to an ongoing list supplied by Johns Hopkins.
A report by the Istituto Superiore di Sanita into the deaths in Italy of 2,003 people confirmed to be positive for coronavirus found that three regions, all in the north, were by far the worst hit.
Lombardy accounted for 71%, Emilia-Romagna 17% and Veneto 3.9%. None of 13 other regions had more than 2% of the total, and 10 of them had less than 1%.
Some studies point to the large number of elderly in the affected regions, and that a large proportion of 18-34s live at home with them. Different demographics in other nations may help to keep the death toll lower.
France began its lockdown on Tuesday morning, requiring citizens to carry official paperwork stating why they were not at home.
French Interior Minister Christophe Castaner told Europe 1 radio on Thursday: "The 15-day period may be extended. If necessary, the government will renew it."
He said that 4,095 fines had been handed out to transgressors and 70,000 control checks made since Wednesday morning. The fine is €135 ($150; £123).
"Some people think they're some kind of modern-day hero when they break the rules – but they're imbeciles, and a danger to themselves," Mr Castaner said.
What else is happening in Europe?
Spain announced on Thursday its coronavirus deaths had risen by 169 to 767 in the past 24 hours, an increase of 28%. Its number of infected people rose by 3,431, reaching 17,147.
Spain is the world's fourth-worst affected country and is under nationwide lockdown.
German Chancellor Angela Merkel addressed the nation on television on Wednesday, which she has previously only done for her annual New Year message.
"The situation is serious. Take it seriously. Not since German reunification, no, not since World War Two has our country faced a challenge that depends so much on our collective solidarity," she said.
Germany has not imposed stringent measures, although it has closed schools and many businesses and public spaces. People can still go out and socialise but German media said her speech appeared to be a final warning to avoid mandatory lockdowns.
Mrs Merkel did not announce new measures but said that could change at any time.
On Thursday Germany reported that its number of coronavirus cases had increased to 10,999. The number of deaths there remains low but has risen to 20, the Robert Koch Institute said.