Vince Cable, the LibDem Business Secretary, went public, making clear he was sympathetic to concerns raised by charities and universities.
He said that, while he supported a crackdown on abusive tax avoidance, it should be separated from genuine charitable giving.
Jeremy Hunt, the Conservative Culture Secretary, is also understood to have expressed worries that the plan to cap tax relief could hit charities hard. He is said to be lobbying Chancellor George Osborne for changes to his proposals announced in last month's Budget.
These would, from next year, impose a ceiling on previously uncapped tax reliefs – including those on charitable donations. The limit would be set at £50,000 or 25% of a person's income, whichever was higher.
But Mr Osborne seems certain to amend his plans after pressure was heaped on him yesterday by charitable groups on both sides of the Border. Criticism has come from billionaire Scots philanthropist and businessman Sir Tom Hunter and millionaire Glasgow entrepreneur Willie Haughey, who have given large sums to good causes.
The Scottish Council for Voluntary Organisations, the umbrella body for good causes north of the Border, said Mr Osborne was effectively branding wealthy givers as tax dodgers. It estimated the Coalition policy could cost charities in Scotland tens of millions of pounds a year.
In a letter published in The Herald today, Martin Sime, the chief executive, writes: "Making giving more expensive and more complicated, and effectively branding our most generous philanthropists as tax dodgers, flies in the face of reason and is incredibly damaging to the life-changing work charities do to help some of the most vulnerable members of society. It's high time the Chancellor admits this is an ill-thought-out policy and exempts charities from the tax relief cap before any lasting damage is done."
Matthew Bowcock, chairman of the Community Foundation Network, which brings donors and community groups together, said the 57 community foundations – which fund local charities across the UK – stood to lose around one-fifth of their donations.
He said: "We estimate, if you add together those who would have given and others discouraged from becoming donors, the charitable sector would be £1bn worse off while HM Revenue and Customs would gain only £200 million."
UK Universities said institutions were likely to be badly affected by the cap as they had received some £560m in donations last year alone.
Nicola Dandridge, its head, explained: "Because universities are the preferred cause of major donors – gifts over £1m – we anticipate they would be particularly hard-hit by the change."
At Westminster, political criticism mounted, with one former Conservative minister insisting: "This must be reversed."
John Whittingdale, the Tory chairman of the Commons Culture Committee, said: "There is a real danger that we throw out the baby with the bath water. The Government has set great store by trying to increase philanthropy in support of the arts and good causes and this clearly won't help."
Conservative backbencher Zac Goldsmith tweeted: "If people use bogus charities to avoid tax, close them. But it's wrong to clobber them all to prevent minority abuse."
Labour leader Ed Miliband also joined the chorus of calls for a rethink, accusing the Prime Minister of trying to "single out those who are trying to do the right thing for a tax rise".
Treasury ministers were yesterday dispatched to the airwaves to try to stem the angry tide.
After Mr Cameron, on a tour of Asia, made clear the Government would look "very sympathetically" at charities' concerns, David Gauke, the Exchequer Secretary, insisted that, while the Treasury would stick by the broad principle that rich people should pay their fair share of tax, ministers would want to work with charities to address their worries.
Danny Alexander, the Chief Secretary to the Treasury, described the policy as good though difficult, pointing out there would be a consultation to "ensure the removal of unlimited tax relief does not have a significant impact on charities which depend on large donations".
He stressed rich people could still give a quarter of their income a year to charity and gain a tax break under the proposal.
But Mr Alexander denied he viewed philanthropists as tax avoiders, adding: "There is tax avoidance in various parts of the tax system and cracking down on that is a key objective for this Government."
Mr Haughey has described the tax as a disaster for charities while Sir Tom Hunter said it was ill- thought-out and punitive.
Meanwhile, Arts Council England warned at least £80m in regular donations to its organisations were at risk.