Postgraduate students should have a "clear and universal" entitlement to financial support for tuition fees, according to a new report.
An expert group set up to look at ways to boost the number of Scottish postgraduate students said changes to funding support would help reduce the barriers faced by many considering further study.
It has recommended prospective postgraduate students should be able to access support to cover the current typical course fee of about £4,594, in addition to the current available living-cost support for eligible students of £4,500.
Between 2004-05 and 2013-14, the total number of Scottish students enrolled in a postgraduate course in Scotland fell by 2,230 (10%).
More than 70% of full-time taught postgraduate students in Scotland fund their own studies.
The report said: "A clear and universal entitlement to student-loan support equal to the typical postgraduate course tuition fee should be implemented for Scottish-domiciled students.
"Eligibility for this entitlement should be consistent with current undergraduate eligibility and it should be available for students up to Masters level for postgraduate courses where the taught element is equal to 50% or above."
The Scottish Government said it would consider the findings of the group, chaired by Professor Bryan MacGregor, vice principal of the University of Aberdeen.
Its recommendations include improved online course information, a greater focus on widening access for under-represented groups, closer engagement between industry and universities, and more incentives to undertake postgraduate study.
Education Secretary Angela Constance said: "We recognise the importance of increased participation in postgraduate study by Scottish students and today's publication outlines a number of ideas on how this might be achieved, which will ultimately contribute to growing Scotland's economy.
"I will now carefully consider the group's report and look forward to working together with the sector to encourage even more graduates to fulfil their potential."
Welcoming the report's findings, NUS Scotland president Vonnie Sandlan said: "As we have long been arguing for, the introduction of greater fee and living cost support for postgraduates will go a long way to opening up postgraduate education to more students and ensuring they can reach their full potential.
"Expecting students to pay up-front tuition fees on top of living costs runs counter to our aspirations to improve access to higher education, at all levels.
"Providing financial support to cover these costs is a vital step in making postgraduate study fairer.
"However, as the report notes, we remain concerned that, without proper regulation of fees, we run the risk of seeing tuition-fee inflation, with universities simply pushing prices up above and beyond the level of fee support available in response to the increased support available."
The report also urged ministers to consider an incentive system where students who receive financial support from the Government to fund postgraduate study pay back a reduced amount or have their student loan debt cancelled "on the basis of gaining employment and making a positive contribution to the Scottish economy".
Universities Scotland director Alastair Sim said: "Today's report makes important recommendations for how we can support more people, from diverse backgrounds, to fulfil their potential at postgraduate level. This is important for individuals and for our growth as a high-skill economy.
"Universities Scotland looks forward to working closely with the Scottish Government early in the new year to build and implement new ways of promoting taught postgraduate study.
"We want postgraduate level study to be within the grasp of all successful graduates with the potential to benefit, no matter their financial circumstances."
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