Edinburgh University’s principal says Scottish students should be allowed to pay towards their tuition, as the sector is in “danger” under the current system.

Prof Sir Peter Mathieson said Scotland’s existing funding model was “not sustainable”, but insisted he was “not advocating the introduction of tuition fees”.

He said that Scotland – where undergraduate tuition is free for most students – could adopt a salary-based “graduate repayment” or ask those who could afford it to pay fees.

The University of Edinburgh is in the middle of a £140m programme of cuts, which has led to a series of staff walkouts since June last year.

Mathieson said the current model could only continue with significantly Scottish government investment per student.

“If you stick with this system of taxpayer-funded education, then it’s perfectly possible to continue that system,” he said.

“But you’ve got to put money into it or you’ve got to change the number of places that are being funded. Both of those are politically difficult.”

“One other alternative is that some of those students make a contribution to the costs.

“They can either do it in the form of tuition fees, or they can do it in the form of some kind of graduate repayment scheme and it can be contingent upon salary.”

Action has been ongoing at Edinburgh University since June, but has been paused after it agreed to halt redundancies for this academic year.

The university announced the programme of cuts in February last year, citing severe financial difficulties.

The UCU union has suggested about 1,800 jobs could be lost due to the university’s cost-saving measures.

This week, strike ballots opened at Aberdeen, Heriot-Watt, Stirling and Strathclyde over threats of job losses and compulsory redundancies

Strike action has also been ongoing over job cuts at Dundee Universitywhich currently faces a £35m deficit.

The Scottish government has already stepped in and bailed out the university with £40m of emergency funding.

Mathieson said the situation at Dundee highlighted the “fragility” of Scotland’s university sector and its reliance of foreign students as an income stream.

He added: “The current system is not sustainable and it’s heading for trouble as illustrated by Dundee.

“I’m sad about what’s happened at Dundee. I think it’s a tragedy for a great university in one of Scotland’s great cities.”

Meanwhile, ministers are being urged to give “serious consideration” to whether Scotland’s four-year degree courses should continue.

Former Labour MSP Des McNulty called for a “broad public debate” in a paper he produced with Prof Huw Morris at University College London’s Institute of Education.

The report suggested the current funding system meant Scottish students were finding admissions “ competitive” at elite universities such as Edinburgh, Glasgow and St Andrews.

The report said the number of places offered to Scottish students was “limited by universities’ need to balance the books” by accepting fee-paying UK and international students.

Annual fees to study in Scotland are £9,535 for other UK students.

Scottish universities, like others in the UK, also charge much higher fees for international students – up to £40,000 per year.

The report also highlighted that Scotland’s four-year university degree system – a year longer than in England – resulted in “additional costs” for both public finances and students.

It requires additional funding for teaching, while students who live away from home have additional living costs for an extra year.

The report suggested reform of Scotland’s four-year degree model to “reduce costs and improve efficiency”.