Trade body Airlines UK has asked the government for an aid package worth several billion pounds.
US travel restrictions will hit all transatlantic routes, further denting an already heavily damaged aviation sector.
The government said it was open to supporting all businesses, including airlines.
In a stark message, Airlines UK said the government’s “prevarication” and “bean counting” had to stop.
“We’re talking about the future of UK aviation – one of our world-class industries – and unless the government pulls itself together who knows what will be left of it once we get out of this mess,” it added.
Airline bosses have been talking to ministers, and executives at Virgin Atlantic are due to write to the prime minister.
The demand comes after the US announced it will extend its European travel ban to include the UK and Republic of Ireland.
The ban, which will begin at 04:00 GMT on Tuesday, will hit vital routes for the likes of British Airways, Virgin Atlantic and Norwegian Air.
Meanwhile, American Airlines announced it is suspending nearly all of its long-haul international flights from Monday.
On Saturday, the Foreign and Commonwealth Office (FCO) advised against all but essential travel to parts of Spain as well as the whole of Poland.
The government said in a statement that it recognises the difficulties UK airlines are facing.
“We are engaging with the sector’s leadership to support workers, businesses and passengers,” it said.
“We have influenced the European Commission to relax flight slots and HMRC is ready to help all businesses, including airlines, and self-employed individuals, experiencing temporary financial difficulties due to coronavirus.”
Under European law, if flights are not operated, designated take-off and landing slots have to be forfeited.
Last week, Virgin Atlantic confirmed it was forced to operate some near-empty flights after bookings were dented by the outbreak.
British Airways warned employees on Friday that the industry was facing a “crisis of global proportions” that was worse than that caused by the SARS virus or 9/11.
In a memo titled “The Survival of British Airways”, the company’s boss Alex Cruz said that it is to ground flights “like never before” and lay off staff.
On Thursday, Norwegian Air said it was set to cancel 4,000 flights and temporarily lay off about half of its staff.