Britain's leading universities want the Government to urgently clarify the post-Brexit rights of EU nationals immediately to allow the sector to plan "with confidence".
The Russell Group has outlined 10 points it believes ministers must answer, warning the lack of clarity is "causing considerable concern" for the thousands of EU nationals employed or studying at universities while also "impacting on our ability" to recruit talented people from the bloc.
Oxford, Cambridge and York are among the 24 universities involved in the group which has insisted there is a need to do everything possible to make these EU citizens feel "valued and supported" to stay in the UK.
Prime Minister Theresa May has outlined plans requiring EU nationals resident in the UK to apply for "settled status", which would effectively guarantee them indefinite leave to remain in the country once Britain leaves the bloc.
The proposed status would be given to any EU citizen who has been living in the UK continuously for five years. Those who have been resident for less than five years would be allowed to stay and apply for settled status when they have accumulated the necessary time.
But the Russell Group has asked for those EU nationals with permanent residence to be "transferred automatically" to settled status, noting: "There is no need to re-assess these individuals' right to be in the UK."
They add students or academics who spend two years or more abroad should not lose their settled status.
EU students starting courses in 2017/18 and 2018/19 must be assured they can stay and work in the UK after finishing their course and be eligible for settled status after clocking up residence of five years, according to the group.
Around 3.2 million EU citizens live in the UK while more than a million British expats reside in other EU member states.
The UK wants the issue to be resolved swiftly, although the EU described Mrs May's offer as a "damp squib" and warned it would give EU citizens fewer rights than their British counterparts.
Russell Group head of policy Jessica Cole said: "Brexit is causing uncertainty and anxiety for EU staff, who need clarity over their future rights as soon as possible.
"There are around 25,000 members of staff from other EU countries at Russell Group universities delivering high-quality teaching and cutting-edge research. We value our EU colleagues and want them to stay.
"EU staff and universities need to be able to plan for the future with confidence.
"We urge the Government to secure an agreement with the EU on citizens' rights at the earliest possibility.
"We want to ensure that families will be able to stay together in the UK and that the system for processing applications will place minimal burdens on applicants at the lowest possible cost.
"There is no reason why individuals and families who have already secured permanent residency should not be granted the new 'settled status' automatically."