Scotland's First Minister Nicola Sturgeon said that raising the starting point at which Scottish workers pay the 40p tax rate was the "wrong choice".
Scottish Labour and the Scottish Lib Dems are also against the plan outlined by UK Chancellor George Osborne.
Scottish Tory leader Ruth Davidson said she did not want to see a sign at the border saying "higher taxes here".
New powers for Scotland means Holyrood can opt not to adopt changes to tax thresholds.
From April 2017, the Scottish government will be able to set both the threshold and rate of income tax, but not the personal allowance.
In the same month, the starting point for paying 40p income tax in the rest of the UK will be raised from £43,000 to £45,000.
This could mean that people earning £45,000 or more in Scotland could be paying an extra £400 in tax than people earning the same amount in England.
At First Minister's Questions, Ms Sturgeon was pressed on whether the SNP would implement Mr Osborne's plan if it was elected to the Scottish government for a third time on 5 May.
The first minister said: "The Scottish government will set out our detailed income tax proposals early next week.
"These will be based on our judgement for what is right for Scotland now and in the long term.
"But let me be absolutely clear today - a large tax cut for 10% of the population, those on the highest incomes, at a time when support for the disabled is being cut, at a time when our public services are under pressure, is in my view the wrong choice."
However, Scottish Labour leader Kezia Dugdale criticised Ms Sturgeon for failing to outline what her party would do with new income tax powers.
She said: "This an important issue about our priorities. Scottish Labour had been absolutely resolute, we would reverse George Osborne's tax cut for the top 15% because when classroom assistants are being cut and teachers are having to buy their own materials, when the gap between the richest and poorest kids is as stubborn as ever, when thousands of people are losing their jobs because of cuts to councils, a tax cut for the better off simply cannot be a priority."
The stance of Scottish Labour is at odds with the UK party. Shadow Chancellor John McDonnell backed the threshold change.
Ms Davidson also raised the Budget tax cut when she quizzed Ms Sturgeon at FMQs.
She said: "I am clear I don't want to see a sign at the border that says 'higher taxed here' because I think that's the wrong choice for Scotland, and I am not the only one.
"In this morning's press Jack Perry, the former chief executive of Scottish Enterprise, wrote that a 'further tax grab will only weaken our tax base and depress the economy - that will do nothing to help support schools, hospitals and the aging population'."
- SNP - Against the 40p threshold change
- Scottish Labour - Against the 40p threshold change
- Scottish Lib Dems - Against the 40p threshold change
- Scottish Conservatives - For the 40p threshold change
Scottish Liberal Democrat leader Willie Rennie echoed Scottish Labour's and the SNP's discontent with the threshold change.
He said: "This Budget was George Osborne's chance to realise his mistake in committing to increase the higher rate tax threshold. But instead he has continued down his well-trodden path to record-breaking tax cuts for the richest in society.
"Scottish Liberal Democrats will never stomach that. When Scotland receives the Smith powers to set tax bands, our priority is a zero-rate tax band, which will effectively extend the personal allowance and lift thousands of people on low incomes out of tax altogether."
What the politicians told BBC Radio Scotland
Labour MP Ian Murray: 'Devolution allows us to take a different approach
SNP Deputy Leader Stewart Hosie: 'This isn't about ideology, this is about fairness'
Treasury Minister Greg Hands: 'We have to live within our means'