BA and Virgin bosses want the same treatment as international rivals
American airlines have asked for a $24bn bail-out, to prevent the industry from going under.
Governments in Europe are facing similar calls from their airlines, in the wake of last week's terror attacks on New York and Washington DC.
In the UK, airline bosses met Transport Secretary Stephen Byers to urge him to give the same level of financial support as foreign rivals.
Richard Branson, chairman of Virgin Atlantic and British Airways chief executive Rod Eddington, said they were encouraged by the government's response, although they did not ask for direct financial aid at this stage.
Improving security
UK airlines also discussed with Mr Byers the need to introduce enhanced security measures in order to build the public's confidence to fly.
Discussions to offer financial aid are already underway in the US and the European Union.
"Massive losses at each of the traditional carriers are inevitable," investment bank ABN Amro said.
"The key issue in the medium term will be survival."
Airlines are expected to shed thousands of jobs in the months to come, as the combination of higher security costs and lower demand from passengers hits an industry already under pressure.
Farming comparison
Advocates of airline aid include Chris Drake of the British Airline Pilots' Association, who said the industry deserved to the same treatment as UK agriculture following the outbreak of foot-and-mouth disease.
"In the same way as British farmers were given support earlier this year, the UK government is duty bound to give our industry short term help," Mr Drake told BBC 2's Working Lunch programme.
BA chief Mr Eddington said the carrier wanted to be able to compete on equal terms with foreign rivals.
"We are very conscious that other airlines around the world will get support, airlines who are competitors of ours both individually and collectively," he said.
It was too early to say what sort of assistance BA might need, he added.
Hand-outs attacked
Virgin boss Sir Richard said: "The government said they did not want to see the industry damaged and will do all they can to help."
Mr Byers had promised a probe into issues including airport tax, insurance and fuel costs, Sir Richard said.
But budget carrier Ryanair, which flies only to European destinations and is likely to suffer less from a fall-off in transatlantic traffic, urged the European Commission to ignore calls for hand-outs.
"State aid to selected state airlines that were loss making before last weeks events cannot be justified by the impact of last weeks events," Ryanair chief executive Michael O'Leary said.
Mr Eddington said neither BA nor Virgin had so far specifically requested financial aid.
The EC revealed concerns for the sector at the end of last week, saying it would monitor events.
But the commission has said it will not change state aid rules, which ban governments from bailing out ailing carriers more than once.
French Transport Minister Jean-Claude Gayssot said on Tuesday he would push for European measures to help the airline sector.
British Airways and other European airlines said they had pulled multi-million pound advertising campaigns following the attacks in the United States.