The Finance Minister Paschal Donohoe has stressed that proposed tax cuts have to happen over "many budgets" rather than just one.
It comes after new estimates revealed the potential costs of Government's tax cut plans.
The Taoiseach last year pledged last year that he would raise the threshold for the 40% tax rate from €35,300 to €50,000.
Figures from the Department of Finance's Tax Strategy Group released yesterday show the cost of introducing the change in a single year would be €2.3 billion.
It suggests a €3,000 increase to all standard rate bands would cost €524m in the first year, and €610m in a full year.
However, it points out that cost could be reduced if the threshold for married earners was increased at a slower pace than for individuals.
The Finance Minister today said the change would have to happen gradually over the next five budgets - and the economy has to keep growing for that time.
He suggested the current thresholds for the higher rate of tax are too low.
Speaking on Newstalk Breakfast, Minister Donohoe explained: "You begin to pay the higher rate of income tax on approximately €35,000 if you're a single income owner, and just over €70,000 if you are a family.
"I do not believe that is a high rate of income within Ireland - it's very much the average wage within our economy."
In terms of the tax cut, Minister Donohoe said he's always insisted the proposed change would have to take place over several budgets.
He explained: "A change of that kind with a cost of that kind was never proposed to be done in one budget.
"The reason why I want to make progress in this objective is that with more people at work... incomes grew by 3% in the first half of this year alone.
"We will see more and more people pay the higher rate of income tax at an average wage if we do not increase the point at which people begin to pay the higher rate of tax."