Liberal Democrat ministers have set out plans for wealth redistribution, urging a crackdown on tax-dodging millionaires and the removal of millions of low earners from tax.

Speaking before the party's spring conference in Gateshead, the deputy prime minister, Nick Clegg, called for the introduction of a "tycoon tax" targeting millionaires who employ "an army of lawyers and accountants" to reduce their bills.

Meanwhile, the chief secretary to the Treasury, Danny Alexander, said he was close to agreeing budget proposals with the chancellor, George Osborne, to remove millions of workers earning under £10,000 a year from tax.

Clegg signalled that he was ready to remove Lib Dem opposition to axing the 50p top rate of income tax – a move Conservative backbenchers and business leaders have demanded – on condition that the wealthiest paid their fair share.

In an interview with the Telegraph, he said he believed thousands of millionaires paid tax at a rate of less than 20%.

"There are hundreds of people earning millions per year who are barely paying 20% tax – forget 40%, forget 50%, forget 30%," he said. "They are not even paying 20%. Therefore I think it's time that we look at what I call a tycoon tax.

"If you're earning millions per year, if you're able to pay an army of lawyers and accountants to basically pick and choose what tax you are paying, if you are paying as low as 25%, 20% or even less in tax, there should be a minimum fair share that you should pay to society.

"It makes people so incredibly angry when you are getting up early in the morning, working really hard to try and do the right thing for your family and for your community, you are paying your taxes and then you see people literally in a different galaxy who are paying extraordinarily low rates of tax."

Aides said no minimum rate had been laid out but that the issue was being discussed ahead of the budget.

Clegg added: "I think the principle of a mansion tax is a perfectly sensible one. The overall approach to bearing down on avoidance, closing loopholes, making sure the wealthy pay more of their fair share than less – that is what is more important to me at the end of the day."

Alexander said raising the tax threshold to £10,000 within the next two years could be paid for by removing pension contributions on the highest-paid earners and closing tax loopholes exploited by millionaires.

He told the Independent: "This [raising the tax threshold] is our priority. I'm proud of the progress that we've already made. We want to go further and faster on that in this year's budget."

Echoing his party leader, Alexander added that he was not "ideaologically wedded" to the 50p tax rate for people earning more than £150,000 a year and suggested the coalition was in the middle of discussions on whether it should be scrapped.

Clegg has already put pressure on Osborne to accelerate the rate at which the income tax threshold is raised. But a report by the economic thinktank the Institute for Fiscal Studies (IFS) said better-off families would benefit most from a rise in income tax allowances, questioning claims that the policy was progressive.

It said the second-richest tenth of families would gain most in cash terms, and that the top half would do best as a proportion of income.

The IFS concluded that the policy was the most effective way of focusing tax cuts on the lowest-paid and would boost incentives to work by taking some out of income tax altogether.

While there are tensions in the coalition over some Liberal Democrat plans to tax high earners and people who own expensive homes, some in the Conservative party seem sympathetic to the thrust of the proposals.

Tim Montgomerie, the editor of the conservativehome blogspot, said on Twitter: "I want a ConsParty that focuses on folk struggling to make ends meet, not those living in big homes that got crazily over-valued during boom.

"Overall Budget wish is faster spending cuts + some wealth taxes to fund shock&awe tax relief for business and families. Is that left-wing?"