WASHINGTON — As the income gap between rich and poor widens, a majority of Americans say the growing divide is bad for the country and believe that wealthy people are paying too little in taxes, according to a new survey.

The poll released Monday by the Pew Research Center points to a particular challenge for Republican presidential candidate Mitt Romney, whose party’s policies are viewed by a wide majority as favoring the rich over the middle class and poor.

The poll found that many Americans believe rich people to be intelligent and hardworking but also greedy and less honest than the average American.

Nearly six in 10, or 58 percent, say the rich don’t pay enough in taxes, while 26 percent believe the rich pay their fair share and 8 percent say they pay too much.

Even among those who describe themselves as “upper class” or “upper middle class,” more than half — or 52 percent — said upper-income Americans don’t pay enough in taxes; only 10 percent said they paid too much. This upper tier was more likely to say they are more financially secure now than 10 years ago — 62 percent, compared to 44 percent for those who identified themselves as middle class and 29 percent for the lower class.

The findings come at the start of this week’s Republican National Convention and as both Romney and President Obama seek to appeal to a broad swath of financially struggling voters who identify as middle class. Romney supports an extension of Bush-era tax cuts for everyone including the wealthiest 2 percent, and says his policies will benefit the middle class by boosting the economy and creating jobs.

“The fact that Romney may be viewed as wealthy doesn’t necessarily pose problems for his candidacy,” said Kim Parker, associate director of Pew Social & Demographic Trends, noting that people see the wealthy as having both positive and negative attributes.

“The challenge for Romney lies more in the fact that large majorities say if he is elected president, his policies would likely benefit the wealthy.”