Chancellor George Osborne today insisted that he would go ahead with controversial plans to axe child benefit for higher rate taxpayers.
Mr Osborne said it was only "fair" that the better off made a contribution towards paying down Britain's record debts.
He indicated however that ministers would be looking at the way the plans are implemented when the changes come into effect next year.
His intervention came after David Cameron sparked speculation of a major rethink when he acknowledged the potential "unfairness" on some families just above the 40% tax threshold who stood to lose thousands of pounds.
Another senior Government minister, Culture Secretary Jeremy Hunt, also said today that ministers were looking at ways to improve the plan and make it "fairer".
However Mr Osborne - who unveiled the changes at the 2010 Conservative Party conference - insisted that he stood by the principle behind the plan.
"We are very clear that it is fair that those who are better off in our society make a contribution to the saving of money we need to make to pay down the debts so we will be removing child benefit from higher rate taxpayers," he told reporters.
"We haven't set out how we are going to implement that and we are going to do that in the next few months but the principle that it is not fair to ask someone who is earning say £20,000 or £25,000 to pay for someone who is on £80,000 or £100,000 to get child benefit is one that I think is very important."
Under Mr Osborne's plan, a couple with three children could lose around £2,500 if one parent earns just a few pounds over the 40% tax threshold of around £43,000-a-year, even if the other is unemployed.
However another couple, where both parents each earn just under £43,000 and enjoy a total household income of more than £80,000, would keep all their benefit.
In an interview with Parliament's The House magazine, Mr Cameron accepted that was seen as unfair by some people and that the changes would create a "cliff-edge" effect for some.
"Some people say that's the unfairness of it, that you lose the child benefit if you have a higher-rate taxpayer in the family (but) two people below the level keep the benefit," he said.
"So, there's a threshold, a cliff-edge issue. We always said we would look at the steepness of the curve, we always said we would look at the way it's implemented and that remains the case.
"But again, I don't want to impinge on the Chancellor's Budget."
His comments were echoed by Mr Hunt who told BBC Radio Surrey: "We are looking at ways to make it fairer. We just want to look at the fairness issue there and see if there's anything we can do to improve it."
Downing Street however stressed the change would go ahead and that Mr Cameron had not changed his mind on the issue.
"He was expressing views that he has expressed before. The change will go ahead," a No 10 spokeswoman said.
"He is still very clear that top end earners should pay their fair share of tax. There is still some time before it is going to be implemented. These are matters for the Chancellor."
Shadow Treasury minister Chris Leslie said: "We have repeatedly warned that the Government's current plans to cut child benefit are unfair and highly bureaucratic.
"These ill-thought-through plans are due to hit families in less than 12 months' time, so David Cameron and George Osborne urgently need to come up with some new proposals."
Alison Garnham, chief executive of Child Poverty Action Group, said: "It is right that ministers are looking at this again, but they are paying the price for rushing out a party conference announcement before asking themselves whether it was fair or workable.
"It would be better to scrap it and find other ways to make the wealthiest pay their fair share, whether or not they have children.
"The Government's plans are riddled with unfairness. The cliff edge means single earner families will be penalised, the targeting of child benefit means families with children will be affected but 70% of higher earners will not, and the three year freeze in child benefit levels means the poorest children will be hardest hit as living costs continue to rise.
"Protecting child benefit is not just about fairness, it's about investing in all our children so we don't damage childhoods, destroy life chances and leave society to pick up the pieces and pay a bigger bill later."