The total number of infections leapt 25% to 7,375 from 5,883, according to the Civil Protection agency.
The jump in figures comes as millions adapt to radical measures introduced on Sunday in an attempt to contain the outbreak.
Up to 16 million people in Lombardy and 14 provinces need special permission to travel under new quarantine rules.
Prime Minister Giuseppe Conte also announced the closure of schools, gyms, museums, nightclubs and other venues across the whole country.
The restrictions will last until 3 April.
The latest figures mean Italy now has the highest number of confirmed infections outside China, where the outbreak originated in December. It has overtaken South Korea, where the total number of cases is 7,313.
Italy has one of the world's oldest populations. The virus is particularly dangerous for the elderly and those with underlying health conditions.
Among the latest people to test positive in Italy is the army's chief of staff. Salvatore Farina said he felt well and was self-isolating.
The strict new quarantine measures affect a quarter of the Italian population and centre on the rich northern part of the country that powers its economy.
The health system is under immense strain in Lombardy, a northern region of 10 million people, where people are being treated in hospital corridors.
"We want to guarantee the health of our citizens. We understand that these measures will impose sacrifices, sometimes small and sometimes very big," Prime Minister Conte said as he announced the measures in the middle of Saturday night.
Under the new measures, people are not supposed to be able to enter or leave Lombardy, where Milan is the main city.
The same restrictions apply to 14 provinces: Modena, Parma, Piacenza, Reggio Emilia, Rimini, Pesaro and Urbino, Alessandria, Asti, Novara, Verbano Cusio Ossola, Vercelli, Padua, Treviso and Venice.
The UK Foreign Office advises against all but essential travel to these areas.
Some transport in and out of the regions affected continued on Sunday. Flights still arrived at Milan's Malpensa and Linate airports, though some scheduled flights were cancelled.
However, Italy's national carrier Alitalia said it would suspend all operations from Malpensa from Monday and Linate would only serve domestic routes. International flights would continue to and from Rome.
The World Health Organization (WHO) chief Tedros Adhanom Ghebreyesus praised Italy for making "genuine sacrifices" with the restrictions. Until Sunday only about 50,000 people in northern Italy had been affected by quarantines.
Last week the government announced the closure of all schools and universities across the country for 10 days.
What is the situation elsewhere?
The number of infections worldwide is more than 107,000, with about 3,600 deaths.
Most of the fatalities have been in China. But the country on Sunday reported its lowest number of new infections in a single day since January - an indication that the virus's spread there is slowing.
Iran, one of the worst hotspots outside China, has now confirmed 6,566 infections and 194 deaths.
However, the real figure is feared to be much higher. One report on Sunday, quoting a government envoy, said there had been 200 deaths in the northern Gilan province alone - but the figures were later removed.
In France, the virus is spreading among MPs. Two more members of the National Assembly have tested positive, officials said late on Sunday.
In total four deputies have been infected. Also on Sunday France reported 1,126 cases, a 19% increase in a day and the second largest number of infections in Europe after Italy.
The French government has banned gatherings of more than 1,000 people.
In other developments:
A man in his 60s has become the third person in the UK to die from Covid-19. The man, who had "significant" underlying health problems, died at North Manchester General Hospital. He had recently returned from Italy.
Saudi Arabia has suspended travel to nine countries including Egypt, Kuwait and South Korea - citizens of those countries will be denied entry to the kingdom. Classes at schools and universities have also been cancelled.
Portugal's president says he will self-isolate at home after meeting pupils from a school that was shut after one of its pupils was admitted to hospital.
US Senator Ted Cruz will also self-isolate after shaking hands with someone who tested positive at the Conservative Political Action Conference last week.
The Grand Princess cruise ship, which is being held off San Francisco in the US, is set to dock in Oakland on Monday.
Oregon became the latest US state to declare a state of emergency after cases there doubled to 14
In the US more than 470 people have been diagnosed with Covid-19, and the death toll is 21.
Among other countries to report a rise in the total number of cases are: Germany (939); Spain (589); the UK (273); the Netherlands (265).
Albania, Bulgaria, Colombia, Costa Rica, the Maldives, Malta, and Paraguay have, meanwhile, all reported their first cases. meanwhile, all reported their first cases.