Introducing social distancing at airports is "physically impossible", the boss of Heathrow has warned.
"Social distancing does not work in any form of public transport, let alone aviation," John Holland-Kaye said.
But the chief executive of Europe's busiest airport said airports will have to introduce health-screening and passengers will have to wear masks.
However, the GMB union said the airport must enforce social-distancing to protect staff and passengers.
The union said workers fear contracting the coronavirus from passengers returning from countries where Covid-19 is prevalent. In the past two weeks three GMB members working at Heathrow have lost their lives to the coronavirus.
In an interview with the Press Association news agency, Mr Holland-Kaye said: "It's just physically impossible to socially distance with any volume of passengers in an airport."
He said a "better solution" is needed to make air travel safe. "The constraint is not about how many people you can fit on a plane, it will be how many people you can get through an airport safely."
In a separate interview, with the BBC, Mr Holland-Kaye said that until a coronavirus vaccine could be developed, airports would have to introduce measures to minimise infection once lockdowns started to ease.
"This might include some kind of health screening as you come into the terminal so that if you have a high temperature, you may not be allowed to fly," he said.
"As you go through the airport, you will probably be wearing a face mask, as people from Asia have been doing ever since Sars (virus) came out."
Ryanair chief Michael O'Leary backed the call for temperature checks. "Anybody with a temperature of over 38 degrees will be refused entry," he told the BBC.
Meanwhile, EasyJet has suggested it could leave the middle seats on its planes empty when flights resume.
The GMB has called for urgent action to protect Heathrow airport workers after an over-crowding incident this week. On Tuesday, two flights arrived at the same time from the same country, the union reported.
It said Heathrow allocated just one conveyor belt for up to 500 passengers waiting to collect their bags.
"No social-distancing was enforced in what was a very crowded area," said Trevlyn McLeod, GMB London region organiser. "These are not safe conditions for passengers and they are not safe working conditions for our members.
"Enforcing social-distancing is essential if our members and airport passengers are to feel that their lives are more important than money," he said.