Lord Mandelson said Mr Clarke's comments contradicted Tory policy
Lord Mandelson has said Tory tax plans have been "thrown into confusion" by shadow business secretary Ken Clarke.
Mr Clarke told the BBC the Tories' main economic goals would be to cut public debt and restore growth rather than cut inheritance tax on homes under £1m.
Later, a Conservative spokesman said the party was still committed to its manifesto pledge to cut the tax.
The Tories' pledge in 2007 to cut inheritance tax was seen as a key point in reviving party fortunes.
Mr Clarke told the BBC's Politics Show the priority was to stabilise public finances and to do so in a way which hopefully did not necessitate tax rises for most people.
Tough choices would be required because of the "tremendous mess" the Tories would inherit if elected, he stressed, with debt levels "of a kind never previously seen".
On inheritance tax, he said raising current thresholds was an "aspiration" which the party retained and hoped to get around to "sooner or later".
Recent indications that the Tories will not reverse Labour's planned tax rises for the rich have already caused internal ructions.
Ken Clarke: "The highest priority is tackling debt"
Business Secretary Lord Mandelson said: "Ken Clarke's comments have thrown [shadow chancellor] George Osborne's tax plans into confusion.
"The thing about Ken is that he just cannot help but say what he thinks.
"On economic and taxation policy, as on so many issues, his views are nearer to the government's than to the Cameron-Osborne Tory Party."
Mr Clarke released a statement denying there was a split over tax policy.
"So far as I am concerned, we are fully committed to raising the threshold for inheritance tax in the first parliament of a Conservative government, as George Osborne has promised.
"This measure will appear in the manifesto and I support it. We also all agree that George Osborne cannot write his first Budget until we have seen what we have inherited. I cannot see any significant difference between what I have said and what my colleagues have said."
Increasing income tax for top earners to 45% from 2011 would be "difficult to avoid", Mr Osborne has said - a stance backed up by Mr Clarke and shadow foreign secretary William Hague.
But the Conservative Mayor of London Boris Johnson has said the move would stifle British enterprise, a view Mr Clarke said was "just wrong".
In recent weeks, senior Conservatives have stressed that the party will face extremely tough choices if it wins the next election given the state of public finances.
The shadow chancellor said he has never ruled out tax rises
The Conservatives insist that cutting the overall burden of tax for families remains a long-term objective and have pledged to freeze council tax bills for two years among other proposals.
But they have declined to rule out tax rises after the next election.
Later on Sunday, a Conservative Party spokesman said: "People should be clear that the promise we made on inheritance tax is a promise we will keep. It will be in the manifesto.
"But for years George Osborne has said he will not write budgets - including the 2010 one - in advance.
"We are only able to help people who have saved to pass on something on to their children because we have identified those who will pay for it - non-domiciles."
BBC political correspondent Carole Walker said the party cannot afford indiscipline on tax.
Our correspondent said: "Ken Clarke's critics will say all this proves they were right to question the wisdom of bringing such an outspoken free-thinker back into the shadow cabinet."
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