Authorities are especially concerned that a surge in cases in Italy’s poorer southern regions, where hospitals are less prepared than the north for such crises, would cause hospitals to buckle. Italy’s health-care system has been weakened by cuts in funding over the last decade, according to Fondazione Gimbe, a medical research firm foundation.

Even in Lombardy, intensive care units are almost at full capacity despite authorities’ efforts to add beds and provide equipment.

“There are no more ICU beds,” said Bergamo Mayor Giorgio Gori in a tweet Tuesday. Mr. Gori said efforts to reorganize hospital facilities and add intensive-care beds may not be enough to cope with a continued sharp rise in cases.

The main hospital in hard-hit Cremona, a town about 50 miles outside Milan, has more than tripled the number of intensive care beds but they are filling up quickly, with about 35 new cases arriving daily, said Dr. Mangiatordi.