Ryanair has issued the government with a seven-day ultimatum to restore airport security measures to normal or risk being sued for compensation.
The budget airline says a larger cabin baggage allowance and fewer passenger body searches would avoid handing "extremists an enormous PR victory".
The "no frills" airline prefers to put less luggage into plane holds to maintain its low prices.
The government said it would not pay compensation or "compromise security".
A spokesman at the Department for Transport said the government does not believe it has to pay compensation under the law.
The DfT said on Friday: "The security regime in place at UK airports is necessary because of the level of security threat and is kept under constant review.
"We have no intention of compromising security levels nor do we anticipate changing our requirements in the next seven days."
The DfT spokesman added that the restrictions were introduced under the Aviation Security Act of 1982, which allows the government to implement measures for the safety and protection of the public.
Ryanair has threatened to claim compensation under a different act - the provision of section 93 of the Transport Act 2000.
Meanwhile, Virgin says it will discuss the cost of extra airport security staff with BAA.
Virgin said it was "not seeking compensation from the government", but thought it should pay for the staff.
Ryanair is keen to encourage more customers
Ryanair chief executive Michael O'Leary described the situation at London airports after the security measures were imposed last Thursday, as a "shambles".
He said: "If they allow these restrictions to stay in place, then the government will have handed the extremists an enormous PR victory."
In launching a campaign to "get Britain flying again" included one million seats for sale on more than 100 routes, priced at £25, one way, including taxes and charges.
The measures the airline has demanded include:
Restoring the hand luggage allowance for passengers leaving British airports to the normal International Air Transport Association (IATA) dimensions of a small, wheeled case, which is just 20% larger than the current restriction of a "large briefcase" dimension
A return to the passenger body searches from the current one in two to the normal one in four.
The disruption to flight schedules because of the alleged bomb plot is estimated to have cost Ryanair up to £2m.
BBC industry correspondent Rory Cellan-Jones said Mr O'Leary was being particularly strident because the "new regulations are a threat to his business".
If Ryanair passengers travel with large pieces of luggage, which have to be checked into the hold "that's a real impediment to his business".
Mr Cellan-Jones explained: "He depends on getting away fast, no baggage in the hold and a quick turn around at the other end.
"If he is kept behind schedule his whole business starts to suffer."
Pilots who believe they should not be banned from taking liquids and gels, including contact lens solution and toothpaste, into the cockpit have now joined the calls for the security measures to be re-examined.
Captain Mervyn Granshaw, chairman of the British Airline Pilots Association (Balpa), said: "Do officials really believe that we need to be prevented from using liquids, given that we freely load and carry many thousands of litres of volatile aviation kerosene every day?
"The measure is illogical and frankly bizarre."
British Airways said it plans to run all of its scheduled flights on Friday, after days of delays and cancellations.
Virgin has also called for a Competition Commission inquiry into the running of British airports in a submission to the Office of Fair Trading.
BAA runs Heathrow and Gatwick, and five regional airports.
The alert, which began on 10 August, sparked strict restrictions on airline baggage.
Passengers are able to take on board one piece of hand luggage which must not exceed 45cm x 35cm x 16cm (17.7ins x 13.7ins x 6.2ins) - equivalent to a small laptop bag or rucksack.
Twenty-three people are in custody in London, after being arrested in raids in London, High Wycombe in Buckinghamshire, and Birmingham last week.
Meanwhile, police are scouring woods in Buckinghamshire, where they found items which could be used to make a bomb.