Barriers to research collaboration in Europe as a result of Brexit would harm scientific progress, says a group of leading UK universities.
Science and research should be a priority in the talks between the UK and the EU, says the Russell Group of research intensive universities.
Any barriers "would be bad for the UK and bad for Europe", said the group's acting director, Tim Bradshaw.
His comments come as the EU prepares to authorise the start of the talks.
Mr Barnier expects the talks to begin immediately after June's general election.
The Russell Group says there will be "no winners" if Brexit results in barriers between researchers and has pledged to work with "all sides to secure a positive outcome".
Dr Bradshaw said there had been "huge breakthroughs in medicine, engineering, and any number of fields" as a result of joint working, which he promised would continue after Brexit.
"We want to maintain the closest possible relationships with colleagues across the EU, and research must be a priority during talks," he added.
He called for the rights of EU students and staff at UK universities to be guaranteed after Brexit.
"We value our EU colleagues very highly and need urgent assurances, that after Brexit, they will retain the same rights to stay and work in the UK that they have now.
"Nearly half of all UK academic articles result from international collaboration and EU member states are some of our biggest partners.
"These relationships improve the quality of UK research and underpin the strength of our science base."
UK universities are among the biggest beneficiaries of the EU's huge Horizon 2020 research fund.
Non-EU countries can also draw on the fund if they contribute to it - but a major condition of countries being able to participate is allowing freedom of movement for researchers, a potential stumbling block in the talks.
The Conservative party manifesto, promises to "collaborate in science and innovation" with EU member states.
The manifesto also pledges to secure the entitlements of EU nationals in Britain and British nationals in the EU.
"There may be specific European programmes in which we might want to participate and if so, it will be reasonable that we make a contribution," the document adds.
Labour's manifesto promises that the party in government would "ensure that the UK maintains our leading research role by seeking to stay part of Horizon 2020 and its successor programmes and by welcoming research staff to the UK".
The Liberal Democrat manifesto warns that "the Leave vote has already started to affect existing and proposed research programmes".
"We will campaign against any reduction in investment in UK universities and for their right to apply for EU funds on equal terms."
Manifestos have not yet been published for the SNP, UKIP or the Green Party.