Universities across the UK are calling for emergency funding of at least £2bn, warning some institutions will go bust without it.
Universities UK says the coronavirus pandemic is threatening to sharply cut overseas student numbers and put universities in financial danger.
They are asking for controls on student numbers in each university, to keep fee income at similar levels to last year.
Universities are promising to honour any offers already made to students.
"Without government support, some universities would face financial failure, others would come close to financial failure and be forced to reduce provision," says a letter from higher education leaders to ministers across the UK.
Alistair Jarvis, chief executive of Universities UK, says the proposals would help universities to "weather the very serious financial challenges posed by Covid-19".
He says academic researchers have made a "huge contribution" to tackling the coronavirus pandemic - and their expertise will be needed in the "recovery of the economy and communities following the crisis".
They are calling for an extra £2bn in research funding and on top of that to provide emergency loans for universities that faced "significant income losses".
"Targeted support" should be available to protect strategically important subjects such as science and medicine, say the industry leaders.
This would be in response to cash pressures from the pandemic:
Universities receive almost £7bn in fees from overseas students - and there are fears that their numbers could be much reduced this autumn
The university sector says it has already lost £790m in cancelled business activities, such as conferences, catering and student accommodation
There is also uncertainty about whether campuses will be able to re-open in the autumn and whether many UK students will defer entry this year
There have been warnings of unprecedented "volatility" in this year's admissions - which, if left unchecked, could see some universities expanding but others left with too few students to be financially viable.
This is a particular risk for universities in England and Wales, which are highly dependent on tuition fee income.
In response, Universities UK is asking for controls on the number of students each university in England and Wales can recruit this year, keeping them to levels expected before the coronavirus outbreak, to stop financially unsustainable swings in numbers.
The scale of concern was suggested in an internal email from a Russell Group university seen by the BBC this week, which warned the university could lose a quarter of its income next year.
The letter from Universities UK to ministers says that to provide "stability" for students currently applying, all offers already made would have to be honoured if students made the required grade.
There is also a call to push back by a year the point at which European Union students are categorised as overseas students, when they will face higher fees and visa restrictions.
Jo Grady of the UCU lecturers' union said the plan was a "piecemeal approach that fails to recognise the size of the problem, or the damage we risk doing to our academic capacity".
Eva Crossan Jory, vice president of the National Union of Students, said any extra funding must support students, "especially considering the mounting discontent that courses are not being delivered as promised and demands for refunds".
She backed calls for the government to "step in" to protect higher education, but said it should include "refunding or all or part of the fees".
"The scale of the financial challenges facing higher education institutions are clearly very serious", said Scotland's Deputy First Minister John Swinney.
He promised to work closely with universities to help them "emerge from this crisis".
A Welsh government spokesman said universities had been "at the forefront of the battle against the coronavirus" and ministers would work to ensure they had the "necessary investment".
In England, a Department for Education spokeswoman said: "The outbreak poses significant challenges to the sector and the government is working closely with universities to understand the financial risks and implications they might face at this uncertain time."