Scottish Green Party co-convener Patrick Harvie said his party might not be able to support the SNP government’s draft budget.
The minority administration could require backing from opposition MSPs to implement its proposed plan.
The nationalists might have expected support from the Greens, which backs Scottish independence.
However, Mr Harvie said the budget failed to have a “progressive approach” to taxation.
He told BBC Radio Scotland’s Good Morning Scotland programme that the SNP “needed to give some ground” and “move some way towards some other party” if it was to win backing for its budget.
Mr Harvie suggested that higher earners “could pay a bit more” if the government chose to reduce the threshold of the higher rate of tax.
- What are Scotland’s tax powers?
- What is in Scotland’s draft budget?
- Brian Taylor on budget bargaining and the tax question
In April, Holyrood will receive the power to set the rates and bands of income tax on non-savings and non-dividend income.
The Scottish government has already said it would not replicate Westminster’s plan to increase the starting point at which workers in England, Wales and Northern Ireland pay the 40p tax rate.
However, it will allow that threshold to increase by the rate of inflation.
Mr Harvie disagreed with that approach and called for the government to cut the starting point for paying the 40p rate.
He explained: “They [Scottish government] could change the threshold in the higher rate.
“They are proposing to increase that, not by as much as the UK, but still increasing it – that represents a tax cut for high earners.”
He urged Scotland’s Finance Secretary Derek Mackay to reduce it instead and “that would mean what high earners have gained gets clawed back and invested in public services”.
Draft budget: How important is the Scottish Green Party’s support?
Analysis by BBC Scotland political reporter Philip Sim
Derek Mackay needs opposition support for his tax plans and his budget – preferably via members voting for them, but if necessary just by them abstaining and not standing in his way.
The finance secretary has been holding detailed talks behind the scenes with opposition leaders, with the Lib Dems and Greens seen as the most likely candidates for a deal.
You can more or less forget about the Conservatives and Labour; neither of them will buddy up with the SNP with hard-fought council elections looming.
It’s now looking more and more like you can count the Greens into that same category.
Patrick Harvie took Mr Mackay to task over tax in this week’s finance committee meeting, and has now doubled down on that position on Good Morning Scotland.
But Derek Mackay isn’t likely to budge on tax. Some bits of spending, maybe, but not tax.
Negotiations will continue in earnest, but these latest developments might leave Willie Rennie as the best placed to strike a deal with Mr Mackay.
He too will have concerns about tax and local services in particular, but it’s possible he could be won over with extra funding for mental health and education.
When Mr Harvie was asked by radio presenter Hayley Millar whether his party would be backing the draft budget, he replied: “I don’t think we can support a budget that has such astonishing cuts to local government services – local services are the ones that people rely on day in day out.
“We need to be investing in those services and protecting the well being of the people who are delivering those services who suffered year after year of real terms pay cut.”
Mr Harvie also reiterated his party’s support for Scottish independence.
He added that “no one” expected a second referendum on the issue to take place this year, but he believed “it should remain on the table”.
Mr Harvie said: “Maybe at some point around the half way mark of the two-year Brexit negotiation period, or not long after that half-way mark, we might need to be in a position to put that question [about Scottish independence] to the public.”