The poll, carried out by the research company Greens Analyseinstitut for the Børsen newspaper, found that while 39 percent of Danes supported lowering tax for those with the lowest incomes, only six percent favoured tax cuts for those in the top tax bracket.
“This unfortunately suggests that the massive socialist propaganda to which citizens are exposed is effective,” Simon Emil Ammitzbøll, the political spokesman for the libertarian Liberal Alliance party, told Børsen.
Ammitzbøll's party is pushing for the top rate of tax to be scrapped as part of the tax reforms the country's weak minority centre-right government is expected to enact in the spring.
Jesper Petersen, the Social Democrats' tax spokesman, celebrated the poll result as “positive news to end 2015”.
“It will be one of the spring's biggest political fights - whether the Liberal Party will succeed in building a majority to reduce tax for the wealthiest Danes,” he told Ritzau.
Denmark's tax system is a complex mix of municipal and state incomes taxes.
In theory, no person, however rich, should have to pay more than 51.95% in national and municipal taxes combined.
But according to the accountancy firm Deloitte, the top rate can in fact reach 56 percent of income.
About 500,000 people are in the top band, making up about 10 per cent of all taxpayers.