The rise in Italy, the main focus of infection in Europe, represents a 25% surge in 24 hours.
Several European countries announced new cases traced to Italy.
Also on Wednesday, the World Health Organization said that for the first time the virus was spreading faster outside China, where it originated.
Globally, more than 80,000 people in about 40 countries have been infected with the new coronavirus, which emerged in December. The vast majority remain in China.
Covid-19, the respiratory disease caused by the virus, has killed more than 2,700 people so far.