A majority of American millionaires support higher taxes for the wealthy to close the economic gap, according to the CNBC Millionaire Survey.

Most of the wealthy also support a higher minimum wage and increasing educational opportunities for the less wealthy to help close the income gap. Inequality is seen as a major problem in the U.S. by 51 percent of millionaires.

Although American millionaires agree on some issues, there is a major divide between views held by Republicans and Democrats, according to the survey of 500 people with investable assets of at least $1 million, which represents 8 percent of American households.

The findings show that, far from being a purely self-interested voting block, American millionaires have complicated views when it comes to the wealth gap and opportunity in America, CNBC says. They are unashamed of their own wealth and attribute their success to hard work, smart investing and saving. They also believe that anyone in America can get wealthy if they work hard.

Sixty-four percent of millionaires support higher taxes on the wealthy and the same number support enhancing savings opportunities for the lower economic classes. Even more, 83 percent, would like to see educational opportunities for the poor and middle-class enhanced.

Most millionaires (78 percent) say the reasons for economic disparity is that the wealthy have greater access to education and two-thirds say the lack of financial literacy prevents poor households from making better financial decisions.

When asked about the top factor in obtaining their wealth, the millionaires ranked hard work first (23 percent), followed by smart investing (21 percent) and saving (18 percent). Education ranked fourth, at 10 percent, followed by frugality and then inheritance. Only 1 percent cited luck as the top reason for their wealth.

Multimillionaires, those with $5 million or more, were more likely to cite running their own business as their top wealth factor. Women were three times more likely to cite inheritance as their top wealth factor, 15 percent versus 5 percent for men, while men were more likely to cite savings, 20 percent versus 14 percent for women.

Most millionaires (94 percent) believe the American dream is achievable, with the largest group (45 percent) defining that as prosperity and upward mobility through hard work.

A millionaire's view on inequality and taxes, however, seems to depend more on politics than wealth, CNBC says. Fully 86 percent of Democratic millionaires say inequality is a problem, compared to only 20 percent of Republicans. Two-thirds of Republicans say anyone can become wealthy in America if they work hard while only one quarter of Democrats agree.

Democratic millionaires are far more supportive of taxing the rich and raising the minimum wage. Among Democratic millionaires, 78 percent support higher taxes on the wealthy, and 77 percent back a higher minimum wage. That compares with 31 percent and 38 percent, respectively, for Republicans.