Bruno Le Maire, France’s economy and finance minister, said the government would not hesitate to buy big stakes in major companies, or even nationalize them, if that is needed to keep them from collapsing. He announced a financial relief package worth about $50 billion, and more than $300 billion in loans for businesses.

Spain’s prime minister, Pedro Sánchez, whose government has already nationalized private hospitals in response to the crisis, proposed an extraordinary $220 billion rescue package for individuals and businesses. That is equivalent to about 16 percent of the country’s economy.

The European Union was considering ditching its notoriously stringent fiscal rules that impose hard limits on member governments’ deficits.

Italy, by far the hardest-hit country in Europe, reported on Tuesday that it had confirmed more than 31,500 coronavirus infections and 2,500 deaths, figures exceeded only by China. Spain topped 11,000 cases, France and Germany each rose past 7,000, and two small countries, Switzerland and Norway, reported infection rates that, relative to their populations, were even higher.

The death of Spain’s youngest victim, Francisco García, 21, a soccer coach from Málaga, struck a particular chord around the country. He had recently gone to a hospital with what initially seemed to be pneumonia, according to local media reports, and doctors found that he had both the coronavirus and previously undiagnosed leukemia. He died on Sunday.

Leaders of the European Union countries, after meeting by teleconference for three hours on Tuesday, agreed to the ban on most visitors from outside the region, setting out on a long stretch of isolation unlike anything in recent European history.

Exceptions will be made for European citizens and residents coming home, although some countries were asking them to self-isolate for two weeks, in some cases away from their families. Medical professionals and scientists will also be exempt.