Universities UK, which represents university vice-chancellors, wants the scheme which gives graduates of Scottish universities easier access to visas to be extended to England, Wales and Northern Ireland. In general, universities across the UK are seeking to end Scotland's competitive advantage in attracting overseas students.
The Scottish Executive policy, part of the Fresh Talent initiative to reverse population decline, allows overseas students a two-year visa extension if they study in Scotland. There were more than 2000 successful applicants in the scheme's first year.
The University of Bedfordshire's vice-chancellor, Professor Les Ebdon, said "International students bring in some £3bn a year to the UK economy, so what we are talking about here is a very important business."
"As far as immigration rules are concerned, we are supposed to be one nation, we don't have devolved immigration rules."
However, he said there was concern the initiative discriminated against other universities, especially in the north of England. Speaking on behalf of Universities UK, he said the scheme offered a "significant competitive advantage" and should be extended.
David Caldwell, director of Universities Scotland, said it was understandable other UK universities wanted to adopt the initiative. He said: "It is not an uneven playing field, it is just a very good scheme. The important thing is that it does not just benefit Scottish universities, it benefits Scotland.
"Scotland needs to attract talent if we are going to have a thriving, growing, knowledge-based economy and these international students bring the country great benefits." He said Scotland would not lose out if the rest of the UK adopted a similar scheme, as there were an "enormous" number of overseas students who were interested in studying abroad.
"I hope for the benefit of our English counterparts that they will get something like it as well. Scotland and England can both be winners."
The Home Office has already watered down the Scottish advantage by introducing visa extensions for overseas postgraduate students in England. They will be allowed to remain in the UK for 12 months without a work permit after completing their studies.
Under the Fresh Talent scheme in Scotland, students have one year from the time they complete their studies to apply and must intend to work in Scotland during the subsequent two years. If they wish to transfer into standard work-permit employment this must be in Scotland and, at the end of the two years, they must either leave the country or switch to a standard visa scheme.
Scotland's population is projected to decline from its present five million to 4.5 million by 2043, according to official figures.
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