Students should pay higher fees to go to university in England, says the Russell Group of leading universities.
The group's submission to Lord Browne's funding review sets out how the £3,225-a-year fee could rise to £9,000 without extra costs in taxpayers' subsidies.
"An increase in graduate contributions is the fairest and only viable option for addressing the funding shortfall," says the Russell Group statement.
Students described the proposals as a "nightmare scenario".
The National Union of Students said this lifting of the cap on fees would mean "mortgage-style debts" of more than £40,000.
The UCU lecturers' union said that such an increase in tuition fees would be "the most regressive piece of education policy since the war" which would "price a generation out of higher education".
The Russell Group wants the level of tuition fees to be high enough to create a range of different charges for different courses - and for students to re-pay loans at a higher interest rate.
This combination of higher fees and reduced subsidies would mean that fees could be raised to £9,000 per year, without extra cost to the Treasury, says the report.
Lord Browne's cross-party review, set to report later this year, is considering how universities in England should be funded.
This includes asking whether there should be any limit on fees - and whether the current maximum of £3,225 per year should be lifted.
The influential Russell Group, representing 20 prestigious universities, has now told the review that the only practical way of funding higher education is to have higher charges for students.
There would also be a reduction in the subsidy on student loans, with repayments at more of a commercial rate.
It argues that the fairest and most effective system is to charge the students whose job prospects will have improved by getting a degree.
It wants higher fees to create a "more differentiated market in higher education", in which the different costs of courses - and potential value to students - would be reflected in the price.
The Russell Group says other alternative sources of funding, such as contributions from business, endowments or philanthropists, will not be sufficient for meeting the financial pressures.
The group says its universities will face a £1.1bn funding gap by 2012-13.
The submission also recognises the political tensions around tuition fees.
The Liberal Democrats campaigned strongly against tuition fees, with party leader Nick Clegg pledging to vote against any rise in fees during the next parliament.
Mr Clegg promised student voters: "Use your vote to block unfair tuition fees and get them scrapped once and for all."
The secretary of state responsible for universities in the Conservative-Liberal Democrat coalition is Vince Cable, who also pledged to vote against raising tuition fees.
He issued a statement in response to the Russell Group's proposal saying that he would await the outcome of the fees review and might abstain if the outcome was not acceptable.
"We recognise the challenges facing the new coalition government but it must not shy away from addressing this urgent problem," says the Russell Group's director general, Wendy Piatt.
The Russell Group argues that tuition fees "have not deterred young people from applying to university".
And it says that university must remain "free at the point of entry" - with debts repaid after graduation rather than charging up-front.
Commenting on the submission, director general of the Russell Group, Wendy Piatt said: "There is an urgent need to secure additional investment in our universities if they are to remain the world-leading institutions that they are today, and to sustain their vital contribution to this country's economic success and prosperity.
"All of the beneficiaries of higher education need to share in meeting this challenge, and while every source of income needs to be explored, this submission shows that an increase in graduate contributions is the fairest and only viable option for addressing the funding shortfall."
The 1994 Group, which represents research-intensive universities, has also called for a reduction in the subsidy on student loans.
Students at Russell Group universities, represented by the Aldwych Group, criticised the call for higher fees.
"The Russell Group has failed completely to put forward any case which suggests that a rise in fees would benefit access to or the quality of education," said Emmanuel Akpan-Inwang, chair of the Aldwych Group.
Oxford University's student union president, Stefan Baskerville, said that "any further proposed increase in fees will lead to the political battle of this government's life".