The new figures suggest a trend reversal as the preceding weeks had been marked by declines in both indicators, Xinhua reported.
The COVID-19 incidence rate -- the number of people testing positive over the total number of people who underwent a swab test in the period -- grew to 19 cases per 100,000 people from 11 a week earlier.
The survey also showed that the number of infections was on the rise in 12 of the country's 20 regions in the past 14 days (ending on July 14).
The overall reproduction number (Rt) was 0.91 in the week of July 7-14 against 0.66 in the previous one.
"The transmission rate is worsening again, and several regions are now moderate risk areas," ISS President Silvio Brusaferro told a press conference.
"Luckily, the impact of COVID-19 on hospitals at this stage remains minimal," he said.
He warned about the potential effects of the Delta variant of COVID-19 in the coming weeks, stressing that contact tracing and quarantining infected people will remain crucial to counterbalance those. Meanwhile, the vaccination campaign is continuing at full steam.
The northeastern Veneto region and the islands of Sicily and Sardinia are the three regions currently reporting the highest reproduction numbers, according to the ISS. Those areas will remain under monitoring, and next week they may even be moved back to the so-called "yellow zone" -- the second lowest tier in Italy's color-coded system with the least amount of COVID-19 restrictions.
Currently, the whole country is in the low-risk "white zone," which means practically no restrictions except for the mandatory use of face masks and social distancing indoors.
In light of the summer holiday period, and especially the higher transmission rate of the Delta COVID-19 variant, the ISS warned that "the transmission number in Italy in August might range between the (minimum) values of 0.58-0.62 and the (maximum) values of 0.8-1.3."