A majority of millionaires support a wealth tax on those worth $50 million or more, but their support declines for a tax on those worth $10 million, according to a new poll.

Fifty-nine percent of millionaires said they would support a new federal tax on wealth over $50 million, according to the Q4 CNBC Millionaire Survey. Democratic presidential candidate Elizabeth Warren's tax plan includes a wealth tax of 2% on wealth over $50 million and 6% over $1 billion.

Forty-eight percent opposed a wealth tax on those worth over $10 million.

Attitudes toward the wealth tax are also strongly dependent on political party rather than wealth levels. Fully 88% of Democratic millionaires support a tax on wealth over $50 million, compared with just a third of Republican millionaires.

As for their own tax burden, most millionaires feel like they pay enough already. Fully 60% feel they pay their fair share of taxes, and a third believe they pay more than their fair share. Republican millionaires are more likely to feel they pay enough or too much.

The richer millionaires are more likely to oppose a wealth tax. About half of those worth $5 million or more oppose Warren's wealth tax.

"Most people who are worth $10 million or less don't feel wealthy, even though they are relative to the population," said George Walper, president of Spectrem Group. "And so they feel they should not be penalized. But they do think that people worth $50 million or more are wealthy and should pay more."

The CNBC Millionaire survey polled more than 700 people with investible assets of $1 million or more, including 301 Republicans, 200 Democrats and 247 independents. Respondents had to be the financial decision-maker or share jointly in financial decision-making within the household. The survey is conducted twice a year, in the spring and fall, and has a margin of error of plus or minus 3.5 percentage points.