Nick Clegg has warned Oxford and Cambridge universities that it is "not up to them" to decide whether they can charge fees of up to £9,000 a year.
The deputy prime minister said they had to "dramatically increase" access for poorer students, after Cambridge said it could demand this amount.
From 2012, English university fees will be between £6,000 and £9,000 a year.
Mr Clegg made the comments to BBC News as he faced an audience of students who accused him of "selling out".
Before the general election, his Liberal Democrats pledged to fight to end tuition fees.
But, since forming a coalition with the Conservatives, this policy has been dropped, amid protests by many students.
Cambridge University's working group on fees has recommended charging £9,000 for all its courses, while leading figures at Oxford have met to discuss the possibility.
During the BBC debate, hosted by political editor Nick Robinson, Mr Clegg said: "The truth is, for Oxford and Cambridge, and for those universities who've said over the last few years that they want to charge £9,000, it's not up to them.
"They can say what they like. They can't charge £9,000 unless they're given permission to do so.
"And they're only going to be given permission to do so if they can prove that they can dramatically increase the number of people from poorer and disadvantaged backgrounds who presently aren't going to Oxford and Cambridge."
Mr Clegg promised that stronger powers for the Office for Fair Access, which monitors entry to higher education, would be announced on Thursday.
The current maximum tuition charge is £3,290 a year, following an increase made by Labour, which first introduced fees in the 1990s.
During his question-and-answer session Mr Clegg was accused by students of having "sold out your principles" and was told by one audience member: "You are either stupid, or you are mad, or you are malicious."
But the deputy prime minister described the coalition's changed fees as a "compromise", adding that many graduates would pay less, and those earning less than £25,000 a year would repay nothing.
He added that, for the first time, those on part-time university courses, like their full-time colleagues, would pay no up-front fees.
Mr Clegg also said: "We think 60% of graduates will never have to pay off the full value of their loans... They will be paying out much less. After a certain period of time they won't have to pay it off at all."
He was accused of failing to understand, as a former pupil at a top public school, what it was like for students from more humble backgrounds - and one student said they feared the creation of a "two tier" education system.
Mr Clegg replied that there was already a "two tier" system, with a gap between the top universities the rest, telling the student: "I am absolutely determined to try to prove to you in the coming years, is that using the leverage that we have got over universities in terms of not giving them permission to charge over £6,000 unless they give greater access to their universities to people like you, I actually think will make the university system fairer."
He refused to apologise for his U-turn over tuition fees, telling the students: "Look, I of course, of course I regret the sheer controversy, the anger and the frustration; I'm not going to apologise for, in these very difficult circumstances creating and helping to create a system which over the years I think will be shown to be a much fairer one than the one we inherited."
He also said he accepted that "the controversy around these policies, some of the lurid headlines, will of course have had an intimidating effect on some young people who are thinking of going to university in the future".
But he added: "There's no money, There's just simply no money... I totally accept that we need to do lots of explaining."
Full details of the requirements on any university charging more than £6,000 will be set out by Business Secretary Vince Cable in a letter to the director of the Office for Fair Access on Thursday.
The letter will say that universities may make greater use of so-called "contextual data", which recognises the achievement of pupils who have had to overcome disadvantage.
Paul Marshall, executive director of the 1994 Group, which represents research universities, said: "Nick Clegg needs to recognise that simply getting people from poorer backgrounds into university is not the only measure of social mobility.
"You need to look at the efforts universities make to avoid high drop-out rates and the value of the experience students enjoy while they are studying.
"Each university needs the freedom to set the fees necessary to deliver the very best for their students. Holding them to ransom over admissions targets alone would be a big mistake. We look forward to seeing some clarity on this tomorrow."