David Cameron warned there must be “a big cultural change” towards sport in schools if Britain is to capitalise on the Olympic success of Team GB.
The Prime Minister called for a return to the "competitive ethos" in school sports and he hit out at teachers who were unwilling to play their part in coaching and mentoring young talent.
Interviewed on LBC 97.3 FM radio, he said that while the Government was investing £1 billion in school sports over the next four years, more needed to be done if Britain was to enjoy continued sporting success in the future.
"Frankly, if the only problem was money, you'd solve this with money. The only problem isn't money," he said.
"The problem has been too many schools wanting to have competitive sport, some teachers not wanting to join in and play their part
"So if we want to have a great sporting legacy for our children - and I do - we have got to have an answer that brings the whole of society together to crack this, more competition, more competitiveness, more getting rid of the idea all must win prizes and you can't have competitive sports days.
"We need a big cultural change - a cultural change in favour of competitive sports. That's what I think really matters.
"And one of the answers there is making sure the sports clubs really deliver in terms of sports in our schools.
"Link the schools with the clubs, because the clubs really believe in competition and the competitive ethos and I think that is one of the best ways to deliver what we want."
Mr Cameron said that while sport had been part of the the national curriculum under the last Labour government, ministers had failed to ensure it was actively encouraged in schools.
"What the last the government did that I think isn't right is if you just simply sit their in Whitehall and set a target but don't actually do anything to help schools meet it, you are not really solving the problem," he said.
"By just saying 'Look, I want you to do this many hours a week' some schools think 'Right, as I've hit that minimum requirement I've ticked the box and I can give up."'
Mr Cameron acknowledged that since the coalition came to power, 21 school playing fields have been approved for disposal - despite a promise in the coalition agreement that they would be protected.
He insisted that in each case it was because the schools concerned were being closed or merged, the land involved was marginal, or it was for reasons of improving sports access.
"It was a mistake that playing fields were sold in the past. They are not being sold any more," he said.
Sport England chief executive Jennie Price said cash was being spent on encouraging youngsters to play sport and provide the next generation of British Olympians.
She told the BBC: "We invest about £250 million a year, a mixture of Lottery and Exchequer - taxpayers' money essentially - into the grassroots of sport.
"People should be very confident that that investment is there and our money is very specifically targeted on participation.
"Our new youth strategy is all about getting young people between the ages of 14 and 25 to play sport regularly."
Mr Cameron's comments immediately sparked anger from teachers' leaders.
Malcolm Trobe, deputy general secretary of the Association of School and College Leaders (ASCL), said the Prime Minister's words were "extremely unfair".
There are a number of factors required for school sport to be successful, Mr Trobe said.
"One is that there's the inclination within a school, and not just within the PE staff, to be involved, and there's a great deal of that inclination there.
"Secondly, there's facilities and, obviously, the selling off of playing fields by both major political parties has not been a good step.
"Some schools have excellent facilities, others have limited facilities.
"Then there's funding. I think it's a bit rich to make a comment like this when one of the most successful schemes was the work done by sports colleges and school sports partnerships, and two years ago that funding was removed by the current Government.
"That was a highly successful scheme."
Mr Trobe added: "It is an unfair comment. The inclination is very much there. There needs to be sufficient funding to enable these networks to work.
"The removal of the funding was a key blow to the continuing success of these sports partnerships."
Mr Trobe said the pressures on academic attainment and increasingly heavy workloads that teachers face need to be accepted and understood by Government.
Chris Keates, general secretary of the NASUWT teaching union, said: "It is unfair to claim that schools are not doing enough to foster a sense of sporting competition among our young people.
"The real issue is the major cuts that this coalition Government has made to school sports. They have cut school budgets in real terms, which has reduced the resources available for schools to spend on sport.
"By ratcheting up the high stakes school accountability regime, ministers have forced schools to focus on a narrow core of academic subjects, which has reduced time in the curriculum for PE.
"If the coalition Government genuinely wants to build an Olympic legacy in this country, it must start by providing schools with the funding and opportunities to ensure all young people can take part in a wide range of sporting activities."
Mr Cameron's comments came as it was revealed that the Government has ditched a target for all state school pupils to take part in two hours of PE and sport a week, as part of a revamp of physical education.
The requirement was introduced by the previous government, and by 2009/10 around 86% of pupils are understood to have been taking part.
A Department for Education (DfE) spokeswoman said the move was part of the Government's aim to cut red tape.
"Instead of handing down target and quotas from Whitehall, we have chosen to trust teachers and parents when it comes to deciding how much sport pupils should do," she said.
British Olympic Association chairman Lord Moynihan said: "Teachers have different agendas and it is right some would not choose to stay on after school to teach sport but there are a lot that would.
"Some don't want to focus on sports as some don't want to focus on arts. We need to give them the tools to the job - the time and the facilities."
Chief executive of the Youth Sport Trust John Steele welcomed Mr Cameron's focus on school sport but said teachers need more resources.
"There is some fantastic work going on in schools to deliver sport from some very dedicated staff," he said.
"What many of these passionate people lack is simply the time and resource to deliver PE and sport as they know it can be. This is what they crave, as they know that much more can be done in schools to improve the delivery of sport."