Professor Andrew Hamilton says tuition fees system is out of kilter and higher fees need not be a barrier to access

Top universities that offer better outcomes for students should be allowed to charge significantly higher tuition fees than institutions that provide an inferior education, Oxford University's vice-chancellor has said.

Professor Andrew Hamilton said tuition fee increases that allowed universities to charge undergraduate students up to £9,000 a year had made little difference to Oxford, which faced a funding "chasm".

In his annual speech, he said Oxford's world-class education would be under threat if no more money could be found to plug a £70m annual shortfall. He called for a new system that would reflect the diversity of education on offer from British universities, and said the current system was "out of kilter".

"The idea of a market – and that is what is ostensibly being created – in which every item, virtually regardless of content and quality, is the same price seems, well, a little odd," he said.

"On the other hand, given the great diversity of the institutions in our higher education system, the notion of different universities charging significantly different amounts doesn't feel inherently unnatural. It is the current situation that seems out of kilter."

A university should be able to charge fees "aligned with what it offers", he said, adding that high fees should not be a barrier to student access if financial support was available and loans were only payable after graduation and linked to earnings.

University figures suggest that around 1,000 students a year turn down a postgraduate place at Oxford because of the financial demands of studying there. Postgraduate students do not automatically qualify for student loans or financial aid.

In January 26-year-old Damien Shannon launched a legal case against St Hugh's College, Oxford, accusing it of "selecting by wealth" by asking students with a conditional place at the university to demonstrate that they held funds to cover tuition fees, plus at least £12,900 a year for living costs.

Hamilton said Oxford's track record on student support was "exceptional" and it offered "the most generous financial package for low-income undergraduates of any university in the country".

He added: "Of course, it is understandable that so much attention is focused on a student's financial circumstances before university, but what happens after is also crucially important. And certainly, so far as Oxford is concerned, all the evidence indicates that the quality of the education a student receives here is overwhelmingly his or her best investment for the future. That in turn means that support for our students in the form of loans from the public purse is also a pretty sound investment."

He did not rule out the possibility that Oxford could raise money by issuing bonds, following the lead of US universities. "None of this means that such a course of action is necessarily right for Oxford and any substantial policy of borrowing – whether as a bond or some other form of loan – would require careful reflection and planning in order to establish clarity about priorities and processes, including how interest payments would be structured and met," he said.

He went on to address accusations that the university had an institutional bias against black and ethnic minority students. The Guardian revealed this year that white applicants to some of the most competitive courses were up to twice as likely to get a place as others, even when they get the same A-level grades.

Figures for applications to the university in 2010 and 2011 revealed that 25.7% of white applicants received an offer to attend the university, compared with 17.2% of students from ethnic minorities. White applicants to medicine, one of the most prestigious courses, were twice as likely to get a place as ethnic minority candidates, even when they had the same triple A* grades at A-level.

Hamilton said the university had "a much more diverse community than you may be encouraged to believe from media stereotypes", with 20% of students from a minority background.

He admitted that figures indicated "that white applicants with similar exam grades tend to fare better than non-white applicants", but said that in some subjects non-white students were more likely to get an offer than white students, and that under-represented groups were more likely to apply for the most competitive courses.

"Any variation can throw up eye-catching but misleading disparities in success rates. Factors like these make hard and fast conclusions both extremely difficult and potentially dangerous," he said.

Hamilton said that last year the university had announced a £1m initiative to promote diversity among academic and research staff after figures revealed that 25% of academic staff and 18% of professorial staff were women.