Just 23 percent disagreed, and the breakdown was virtually the same across age groups and among both weekly Mass-goers and those who attend church less frequently.
The national poll conducted the last week of September also showed that American Catholics have a favorable (53 percent) or very favorable (36 percent) opinion of Francis, and just 4 percent view him negatively.
"American Catholics liked what they heard when Pope Francis said the church should stop talking so much about issues like gay marriage, abortion and contraception," said Maurice Carroll, director of the Quinnipiac University Polling Institute.
The survey also found that Catholic support for same-sex marriage continues to be strong, as other surveys have found, with six-in-10 Catholics approving of gay marriage and 31 percent opposed. That's slightly above the national 56 percent approval rating.
But the latest research also indicates that support for same-sex marriage only drops slightly among weekly churchgoers, to 53 percent, with 40 percent opposed. That finding could cause consternation among social conservatives who argue that the most devout Catholics tend to support the hierarchy's position against gay marriage.
Another finding likely to provoke concern among tradition-minded church leaders: Catholics support the idea of ordaining women priests by a 60-30 margin; it only drops to 52-38 percent among those who attend service about once a week. There is almost no gender gap in that support.
The number of Catholics surveyed was not large 392 adult Catholics out of an overall selection of 1,776 respondents, and the margin of error is plus or minus 5 percentage points. But the trend lines seem to be in keeping with other research.