Blair allegedly made the remarks privately to Rupert Murdoch, chairman and chief executive of News Corporation, which owns the rival Sky News.

The comments threatened a new rift between the government and the BBC following the Andrew Gilligan affair over events leading to the Iraq war and recent criticisms of ministers Today presenter John Humphrys, which were controversially leaked to the press.

Downing Street said last night it had no comment on the report in the Financial Times. The BBC said that its coverage had been 'committed solely to relaying the events fully, accurately and impartially'.

Murdoch, a long-standing critic of the BBC, was addressing the Clinton Global Initiative conference in New York. Chuckling, he said: 'I probably shouldn't be telling you this' before recounting a recent conversation with Blair. He said the Prime Minister was in New Delhi when he criticised BBC coverage of the catastrophe in New Orleans: 'He said it was just full of hatred of America and gloating at our troubles.'

Bill Clinton, the former US President who was hosting the conference, also attacked the tone of the BBC coverage at a seminar on the media. He said it had been 'stacked up' to criticise the federal government's slow response.

Sir Howard Stringer, chief executive of Sony Corporation and a former head of CBS News, said he had been 'nervous about the slight level of gloating' by the corporation.

The disapproval will come as a blow to BBC executives, who had declared themselves delighted with the hurricane coverage, led by Matt Frei. They believed they had learnt the lessons from the Boxing Day tsunami in Asia, when the BBC was regarded as being slow off the mark.

Blair's reported comments were strongly criticised last night by Martin Bell, the former BBC war correspondent and former MP.

Bell said: 'Assuming it's accurate - it may of course be that Tony Blair was simply telling Rupert Murdoch what he thought he wanted to hear. If he really does have a gripe with the BBC coverage, there is no shortage of forums in which he can say so publicly. But the last time he picked a fight with the BBC, as I recall, the government came off rather badly.'

He added: 'I think Matt Frei's reporting was absolutely immaculate and reflected the fact that one of the things the BBC is there for is to report events as they happened rather than as politicians may want them perceived to have happened. If Tony Blair does want to confront the BBC over this, I'd be surprised - because he would find absolutely zero support, except perhaps among his usual henchmen.'

Charles Wheeler, the veteran former US correspondent for the BBC, said: 'I don't believe Murdoch actually said that. It doesn't sound like Blair to me. The coverage I saw was extremely good and got better and better. Matt Frei was very good. He got quite angry, which is what might have annoyed people.

'I don't see why people should be unemotional; I never was. You have to tell people what you feel and what you hate - that's part of legitimate reporting.'

A spokesman for the BBC said last night: 'We have received no complaint from Downing Street, so it would be remiss of us to comment on what is reported as a private conversation.'