The universities minister has given his clearest indication yet that students could soon be forced to pay higher tuition fees.

In an interview with the Guardian, David Willetts warned that the cost of hundreds of thousands of students' degree courses was a "burden on the taxpayer that had to be tackled".

Willetts said he did not want to pre-empt the recommendations of Lord Browne's independent review into whether fees should rise from £3,225 a year. But he added that students should consider university fees "more as an obligation to pay higher income tax" than a debt.

His words angered the National Union of Students (NUS), whose president-elect, Aaron Porter, said Willetts had failed to understand that graduates were leaving with debts of £22,000 on average and that this felt "very much like debt to them".

A debate over fees will cause huge divisions in the coalition government. While Willetts has strongly suggested they might rise, the Liberal Democrats have promised to scrap "unfair" tuition fees.

Willetts said the system – whereby universities charge fees, the Student Loans Company pays them and students repay only when they have graduated and earn over £15,000 a year – was "unsustainable" and in need of "radical change".

Labour had "catastrophically failed" to explain to students how the system worked, he said, and the universities were given too few incentives to focus on excellent teaching, he added.

"It is not a matter of simply changing the fees," he said. "The system doesn't contain strong incentives for universities to focus on teaching and the student experience, as opposed to research."

Nick Clegg, the Lib Dem leader, and Vince Cable his former deputy have pledged not to vote in favour of higher fees. To avoid division, the coalition government has agreed to allow Lib Dems to abstain from voting on the issue in parliament. The review into fees, which is being led by Browne, the former chief executive of BP , is likely to report in the autumn.

A coalition document, published last month, outlined the government's priorities. It included ensuring the sector was properly funded, increasing social mobility and advancing scholarship. Ahead of a speech he will give to Oxford Brookes University tomorrow, Willetts said: "The so-called debt [students] have is more like an obligation to pay higher income tax."

He said he had asked the Higher Education Funding Council for England to write to all higher education institutions requesting they publish their records of how many graduates are in jobs and how they prepare students for the workplace.The aim is to have the information ready for 2011, he said.

He added that he wanted teenagers to consider apprenticeships as a possible route into higher education.