The survey, which was conducted by Ipsos and published in Corriere della Sera on Sunday, found that almost two thirds of Italians supported Renzi – a three percent increase since July.
Faith in the activities of the government also remained solid, with 58 percent expressing positive views.
But while the prime minister and government have won the hearts of many Italians, his reforms have not proved to be so popular.
Just 42 percent said they supported his plans to boost economic growth, with 46 percent expressing negative views.
Meanwhile, 42 percent supported his reform of public administration and 48 percent expressed positive views about his school reform.
There was good news regarding the new appointment of Italy’s Foreign Minister Federica Mogherini, who two weeks ago was appointed EU foreign policy chief, with 49 percent percent of Italians expressing their support compared to just 28 percent of negative reviews.
Since Renzi came to power in February there has been growing scepticism about the former mayor of Florence's ability to deliver against a backdrop of economic figures that make grim reading.
Economic growth has just turned negative for the third time since the financial crisis erupted and sent Italy into a particularly vicious tailspin.
Over that period, the whole economy has shrunk by nine percent. National output is no greater now than it was in 2000. Industrial production has fallen to levels last seen in 1980.
At the end of August, Renzi held a back-to-work cabinet meeting, billed as the first of what the prime minister says will be 1,000 days of reform designed to free the country from the dead of institutional inertia and lay the foundations for a renaissance of the moribund economy.