ROME — Italy got the message.

On the first day of Europe’s first nationwide restriction on movement and public gatherings to stem the rampant spread of the coronavirus, Italians steered clear of their streets, shops, churches and soccer fields.

They obeyed the government’s “I Stay Home” decree, announced on Monday night by Prime Minister Giuseppe Conte with a plea for common sacrifice to safeguard the country’s elderly population and to save the health system from collapse.

But even as Italians stayed inside, officials in the country’s north, the front line of the outbreak, pleaded for still stronger measures that would essentially shut down all commercial activity and public transportation in an effort to suffocate the contagion.

It was “time for firmness,” said Attilio Fontana, the governor of the Lombardy region, which is home to Milan and many of the most infected towns. Officials suggested the total shutdown could last for two weeks, and a spokesman for Mr. Fontana said he hoped the request would be approved by the government in Rome “as soon as possible.”