MSPs have said they believe a “pragmatic solution” can be found to a row over post-study work visas.
The visas allowed non-EU students to remain in the UK for at least two years after graduating from a British university or college.
But the UK government scrapped the scheme in 2012, citing “widespread abuse”.
All five parties at Holyrood have since backed the reintroduction of the visas in Scotland.
A report by a cross-party group set up in the Scottish Parliament to examine the issue has now published a report which makes ten recommendations covering who should qualify for the visas and the conditions they should meet.
The group said the recommendations set out a “clear and practical path to allow talented graduates to remain in Scotland”, and called on the UK government to “consider them seriously”.
The Home Office has previously told BBC Scotland there were “no plans” to reintroduce the visa system, which it said had “undermined the UK’s work migration routes and damaged the reputation of our education system”.
It has also said that the UK has “excellent” post-study work opportunities for students who wish to stay and work after graduating, and that graduates can stay if they get a graduate-level job, an internship or become a graduate entrepreneur.
Under the current rules, students from outside the EU are allowed to stay in Britain for four months at the end of their courses, and if they get graduate jobs they can switch from student visas to work visas.
But Scottish Secretary David Mundell said in January that the UK government had not shut the door on the possible reintroduction of post-study work visas in Scotland, and that it was “open to reasonable suggestions” over the issue.
In its report, the steering group, which contains MSPs from all of the main political parties as well as business and education representatives, said it remained convinced that a “flexible post-study work route would benefit Scotland”.
Its recommendations included:
People who have completed an HNC, HND, degree or post-graduate qualification at a Scottish institution should be eligible for a post study work visa
People who have a visa should transition onto a job at the same level as their qualification, but the visa should also provide flexibility to take up other job opportunities
The post study work visas should last at least two years
People on post study work visas should have some savings to tide them over in a crisis, but should be able to spend these savings when they need to without losing their visa
Time spent in Scotland on a post study work visa should count towards being able to stay permanently in Scotland after five years
Partners and older children of people on post study work visas should be able to work in Scotland, if they want to, as per current immigration guidelines.
The report also stated that people on post-study work visas “will already have excellent English language skills” in order to have completed their qualification, so no additional English language requirement would be needed.
And it recommended that the new visa scheme should be evaluated and changed if improvements can be made.
‘Checks and balances’
Speaking on behalf of the group, Minister for Europe and International Development Humza Yousaf said there was “overwhelming” support for the visas in Scotland.
He added: “Our recommendations introduce a reasonable degree of flexibility, while maintaining rigorous checks and balances.
“Scotland’s immigration needs are different to those of the rest of the UK and the return of the post study work visa would be an important economic lever of great benefit to Scotland.
“Allowing talented students to remain in Scotland after graduation will help us grow our working age population and support and strengthen our economy.”
The Scottish government has also been campaigning for a return of the visa, which allowed international students from outside the EU to remain in Scotland and work after graduation.
And the Smith Commission, which was set up to look at more powers for Scotland following the independence referendum, said the Scottish and UK governments should explore the possibility of introducing “formal schemes to allow international higher education students graduating from Scottish further and higher education institutions to remain in Scotland”.