A furious row has broken out after the Liberal Democrats accused Nicola Sturgeon of wanting to cut the amount workers can earn tax-free.
Thousands of Scots have been taken out of tax altogether after increases to the personal allowance in recent years.
Yesterday Scottish LibDem leader Willie Rennie said the SNP leader's call for control over the allowance's level showed she wanted to bring in a "new tartan tax for hard-pressed workers".
That was angrily denied by the SNP, who said the power could help ease the Tory-LibDem Coalition's "punitive austerity agenda".
Last week's Smith Commission report into historic new powers for Scotland recommended income tax be devolved to Holyrood, but said the personal allowance should be retained by Westminster.
LibDem sources said that, under the new powers, Scottish ministers could take even more workers out of tax if they introduced a new "zero rate" of income tax, set above the personal allowance level.
The only reason to want control over the level itself would be to lower it, they said.
Mr Rennie said: "Demanding the personal allowance must mean the SNP want to increase tax. They should come clean."
He added: "The last thing low earners need just now is to pay more tax but it seems that is what the SNP want to do. A new tartan tax for hard-pressed workers is the last thing Scotland needs."
A spokesman for the First Minister said: "The reason we want Scotland to have full responsibility for all tax and welfare is simple - to create a more prosperous and fairer country, and to stop the punitive austerity agenda which the LibDems are helping the Tories implement at Westminster and which is causing such hardship for so many people across Scotland."
Earlier Ms Sturgeon warned the new powers failed to include "one of the key levers you could use to lift people out of poverty" - the personal allowance.
She also said voters could help Scottish ministers win extra powers by backing the SNP in May's General Election.
"I think now the Scottish people can decide if they want to use the power of their votes in the General Election to up this offer and get more powers devolved to Scotland," she said.
It is understood the SNP plan to include calls for the minimum wage, more benefits and the income tax personal allowance to be transferred to the Scottish Parliament in its General Election manifesto next year.
At the weekend the SNP traded blows with the Unionist parties amid growing attacks from both sides over how the Smith proposals were arrived at.
The SNP have accused the other parties of watering down plans that would have seen Scotland given more powers over areas such as welfare.
Labour hit back, claiming the SNP backed a last-minute attempt to cut the right to create new benefits from the final document.
There were also reports yesterday that Labour had threatened to walk out if abortion had been devolved to Scotland.
Meanwhile, Ukip figures have threatened to veto the Smith agreement if they hold the Westminster balance of power in 2015.
lThe leaders of 119 councils in England - 65 controlled by Labour - have warned the English will not accept devolution unless it is matched by an equal redistribution of power south of the Border.
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