Dundee University has called on SNP ministers to reveal whether they plan to charge EU students to study here.
Bosses at the institution fear the world-class reputation of Scottish universities could be damaged if access to European talent is restricted.
John Swinney, the Education Secretary, has already pledged that EU undergraduates joining Scotland’s universities in 2017 will benefit from free tuition throughout their courses, as well as those already studying here.
Speaking after a meeting between ministers and representatives from higher education, a spokesman for Dundee University urged him to go further.
The spokesman said that “despite the clear challenges ahead” there is an “opportunity to show that Scotland still welcomes the world”.
“The Scottish Government can help in this regard by making clear its approach to the fee status of EU students as soon as possible and by lobbying the UK Government on free movement, the status of current EU staff and research funding,” he said.
Brexit would end the requirement to offer the same free tuition to EU students that Scots are entitled to, which currently exists under anti-discrimination rules laid down by Brussels.
Higher education minister Shirley-Anne Somerville said: “The continued lack of clarity from Westminster is hampering planning and, against this backdrop, it is difficult to pinpoint an exact date when we will be in a position to decide future policy on this specific issue.
“That is why we continue to work with the higher education sector to urge the UK Government to provide assurances that the immigration status and rights of EU nationals currently living in Scotland, or who wish to work or study here in future, will not change in the future.”
Theresa May has said it would be wrong to guarantee EU nationals can stay without a reciprocal agreement from other member states for Brits.