The rise was closely linked to travel and summer entertainment for holidaymakers, according to an official report.
Italy recorded 1,210 cases on Sunday, compared to 642 on Wednesday, latest official figures showed.
On Saturday, 1,071 new cases were recorded, with 947 cases registered on Friday and 845 on Thursday.
The biggest number of cases was recorded in the northern Lombardy region with 239, followed by the Rome region where there were 184 further cases and the Venice region which had 145.
A further seven deaths were recorded on Saturday, bringing the total number of Italian coronavirus fatalities since the start of the pandemic to 35,437.
Despite the steady rise in cases, Health Minister Roberto Speranza ruled out any general return to lockdown, saying the situation was under control.
The country currently has 18,438 cases including 69 patients in intensive care.
More than 200,000 Italians have recovered from the illness in recent months. Ranieri Guerra, assistant director general of strategic initiatives at the World Health Organization, has said the increase in cases is partly explained
by an increased use of tests.