Mr Blair made the remarks as Labour published new education policies designed to show that the party will be tougher on bad schools and teachers than the Conservatives.
Teachers said Mr Blair's figure was wrong and accused him of "teacher bashing".
While headteachers attacked Mr Blair for "a slip of gargantuan proportions", the Office for Standards in Education said only 2 per cent of schools were officially "failing"; a further 10 per cent had serious weaknesses.
Teachers also criticised Labour's paper on raising standards for concentrating too much on streamlining procedures to get rid of bad teachers and too little on providing more money for schools.
Labour proposes a new headteacher qualification, a new grade for the best classroom teachers and a "fresh start" for bad schools which would be closed and reopened with a new name, a new head and new governors. There would be national guidelines on homework and on testing five-year- olds.
Mr Blair said at the launch of the paper, Excellence for All: "There is no more important issue than raising standards in our schools - particularly the 30 per cent of schools that are failing.
"Britain stands 35th in the world education league. It is a disaster for British firms trying to compete abroad. And it is a tragedy for all those talented children ... not achieving their full potential. There will be zero tolerance of failure from any government I lead."
David Blunkett, Labour's education spokesman, said the figures were based on inspectors' reports and national test results.
David Hart, general secretary of the National Association of Head Teachers, said Mr Blair's remarks were "a slip of gargantuan proportions and fundamentally untrue. It doesn't help in delivering a positive message to a teaching force desperately in need of motivation".
Mr Blair appears to have used the figure given in inspectors' reports for the percentage of unsatisfactory lessons - around 30 per cent - to back his remarks.
Mr Blair said there were thousands of good teachers and he hoped very much to have a constructive dialogue with the profession. "But you can't in the end have a situation where there are people running schools who can't do it properly. If we aren't prepared to take that on board as a country, then we are betraying our own future." Mr Hart said teachers could not be sacked more quickly without falling foul of the Employment Protection Act.
The Liberal Democrats said Labour had still not promised more money for schools and urged the party to join them in voting against tax cuts that would lead to school cuts.
Nigel de Gruchy, general secretary of the National Association of Schoolmasters/ Union of Women Teachers, said: "There is not a snowball's chance in hell of realising these plans without substantial additional expenditure."
Mr Blunkett promised "a quantum leap" to bring schools standards up to the level of our economic competitors. "Our crusade is designed to offer to the many what previously was only available to the few."
In the Commons at Prime Minister's question time, Mr Blair asked Mr Major: "Rather than encouraging a small number of children to leave the state sector for the private sector, should we not be raising educational standards for the seven million children in the state sector?"
John Major accused Labour of turning its back on its own former policies, and said Labour had opposed most of the Tories' attempts to improve standards.
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