The poll by Demos came as bishops in Austria asked the Vatican to hold discussions on the issue of priestly celibacy, The Times of London reported.
In the poll, 65.9 percent of Italians interviewed said they were "very much" in favor or "fairly" in favor of abolishing the church's celibacy rule and 22 percent said they were opposed to priests marrying.
The survey suggested confidence in Pope Benedict XVI in Italy had dropped from 53.7 percent in 2007 to 46.6 percent now. The poll suggested confidence in the church had dropped from 59.2 percent a decade ago in Italy to 47.2 percent now.
Overall, 62 percent said the church had minimized or hidden clergy sex-abuse scandals. Eighteen percent said criticism of the church over sex abuse was "unjustified" and 13 percent said the church had handled the problem "adequately."
Sunday, 200,000 people filled St. Peter's Square in a show of support for the pope, who called the rally a "beautiful and spontaneous show of faith and solidarity."