Italian Prime Minister Giuseppe Conte warned Thursday that the European integration project was at risk if EU member states do not find an economic response to the coronavirus crisis.

"If we do not seize the opportunity to put new life into the European project, the risk of failure is real," Conte told the BBC as finance ministers bickered over over a common strategy in Brussels.

Italy and other southern European nations hardest-hit by the pandemic want Brussels to release generous financial aid to help idle businesses and the unemployed cope.

An ill-tempered Eurogroup videoconference ended after 16 hours on Wednesday with the Netherlands demanding that nations meet tough economic conditions to qualify for the aid.

Conte repeated his call for Europe to rise and meet its "biggest test since World War II".

Hard-hit Italy was the first European country to shut down almost all business activity on March 12 because of the virus.

The closures and accompanying containment measures have helped stem the spread of a disease that has officially claimed 17,669 lives across the country since February, the world's highest toll.

The Italian government is now weighing how and when to ease social distancing measures that have so far been extended until April 13.

Conte said he was still looking to the government's scientists for counsel about which businesses and factories might be safe to open first.

"We need to pick sectors that can restart their activity," said Conte.

"If scientists confirm it, we might begin to relax some measures already by the end of this month."

Italian media speculate that some of the strictest measures might be lifted in stages starting on April 26 and then again on May 3.