The poll, conducted online by SWG market researchers, found 55 percent of those polled say they support Napolitano, Italy's ANSA news agency reported.
About 80 percent of center-left voters said they have confidence in Napolitano while 59 center-right voters said the same.
Only 28 percent of supporters of the anti-establishment 5-Star Movement said they supported the 87-year-old president.
Napolitano was re-elected Saturday after five ballots failed to elect a successor. He became the first president of Italy to be elected to serve a second term.
The poll had a margin of error of plus or minus 3.1 percentage points, ANSA said.