Prime Minister David Cameron has rejected suggestions the government is considering allowing wealthy students to pay for extra university places.
"There is no question of people being able to buy their way into university," Mr Cameron told the BBC.
Universities Minister David Willetts said extra places could be funded by businesses or charities and not wealthy individuals.
But Labour's John Denham accused the government of a "humiliating u-turn".
Mr Willetts had to face questions in the House of Commons over proposals to create extra university places in England which would not depend upon public funding.
In angry exchanges, the minister told MPs that he was considering plans to make it easier for employers and charities to fund additional places - but "rich individuals should not be able to buy their way into universities".
Shadow Business Secretary John Denham attacked the government for a "humiliating climbdown" - and said there were many questions unanswered how any extra places would be allocated.
"I think it is clear that the government still intends to create a two tier system - one method of entry for the most able, another for those with access to private funds from one source or another," said Mr Denham.
There were also questions from MPs about what types of organisations could sponsor their own extra places - would it include independent schools with charitable status or trusts set up for their children by wealthy families.
Mr Cameron had earlier moved to quash the idea that there should be a different system of places for wealthy students - saying that Mr Willetts had not intended that.
"That is not going to happen. That is not our policy... The government's policy is absolutely clear that university access is about the ability to learn and not the ability to pay," said Mr Cameron.
At present, universities can create extra places and set their own fees for overseas students - and there were suggestions that a forthcoming White Paper would allow such flexibility to be extended to wealthy UK students.
This would mean that universities would be able to create more places for self-funded students, outside of the quota of publicly-funded places.
Speaking on BBC Radio 4's Today programme, Mr Willetts had said: "People are coming to us with innovative ideas about how you could liberalise the system - so that it would be possible for extra people to get to university."
Any such proposals would have to comply with the government's support for social mobility, he said.
But with such strong political sensitivity around tuition fees and social mobility, the government was forced to clarify that such changes would not mean any priority university entrance for the privileged.
"There is no question of wealthy students being able to buy a place at university. Access to a university must be based on ability to learn not ability to pay," said a statement from Mr Willetts.
There had already been an angry reaction from students and lecturers at the prospect of extra places being created for students rich enough to fund themselves through a degree course.
Aaron Porter, president of the National Union of Students, said such a scheme would "create a two-tier system that allows the richest, less able applicants a second bite at the university cherry and denies low and middle-income students the same opportunity".
"It simply cannot be the case that daddy's money can buy you a place at this university. Off-quota places are a badly disguised attempt to completely remove the cap on fees," said Rahul Mansigani, president of Cambridge University students' union.
'Turning back the clock'
"Far from increasing social mobility, it is hard to see how this is anything other than the government entrenching privilege for the wealthy in response to its failing university fees policy," said the UCU lecturers' union leader, Sally Hunt.
"We risk turning the clock back to a time when breeding rather than brains were required to get on in life."
"This manifestly unfair and elitist policy smacks of total desperation from a government whose universities policy is in freefall," said David Barclay, president of Oxford University Student Union.
Sir Peter Lampl, chairman of the Sutton Trust education charity, said: "This proposal is likely to deal a serious blow to social mobility, allowing the better-off to buy advantage in the university system, just as they do in the school system."
But there was also support for the idea of allowing universities greater freedom over creating extra places.
Andy Westwood, chief executive of the Guild HE group of universities, said that it could give universities more flexibility over the number of places they could offer for poorer students.
"Providing off-quota places can be socially progressive," said Mr Westwood.
"With the right incentives, this could lead to more innovative and flexible choices such as part-time, intensive and modular courses, with 'pay as you go' options," he said.
The proposals are being considered as part of a government White Paper on higher education set to be published next month.
At present, the government sets a quota for publicly-funded university places each year - and the idea of "off quota" places is that universities could create additional places for those students who did not have to borrow loans to pay tuition fees.
There are already companies such as KPMG which have plans to sponsor students through university - creating such "off quota" places.