Heathrow has said that major infrastructure investors will turn their backs on the UK if regulators do not allow them to make a fair return on their money.
The airport is making its case in a last-ditch attempt to persuade the Civil Aviation Authority to soften its stance.
The CAA will determine on Thursday how much Heathrow and other regulated airports, including Gatwick, will be allowed to charge airlines to use their facilities for the next five years.
Heathrow chief executive Colin Matthews believes all the signs are that the CAA's proposals will be the toughest the airport "has ever faced".
They will threaten investment in Heathrow and other infrastructure projects, he warns.
The regulator has suggested price rises at Heathrow should be capped at 1.3% below the retail prices index measure of inflation between April 2014 and 2019.
The maximum return on investment that would be allowed under the CAA's current proposals would be 5.35%.
"This is below what investors in airports in Rome, Frankfurt and Paris could expect to generate," Matthews writes in an article published on the Daily Telegraph's website.
He concedes that airlines, which pass airport charges on to passengers, should not have to pay "a penny more than is necessary".
But Matthews says the current regime of suppressed prices is "not sustainable" if passengers and airlines want Heathrow to continue improving facilities.
Heathrow's investors have been making returns of less than 1%, he adds.
"The point is coming when Heathrow's investors will tire of making no return," he says. "They don't have to keep ploughing money into the UK.
"Heathrow's investors include the sovereign wealth funds of China, Qatar, and Singapore, as well as investors from the US, Canada and Spain.
"These are global players with deep pockets and countries all over the world compete for their investment funds. And their experience at Heathrow is putting them off investing in the UK."
Heathrow is seeking to raise landing charges by 4.6% above the rate of inflation for the five years from April 2014.
"Passengers will see prices rise by less than £1 per ticket a year in return for £3 billion of investment in new facilities, including the completion of a new Terminal 2 building.
The airport has warned that if the CAA's price caps are enforced it will only be able to invest a maximum of £2 billion, which will go towards maintaining facilities rather than improving them.
International Airlines Group chief executive Willie Walsh last week called for Matthews to step down if he can't maintain investment at £3 billion while accepting lower tariffs.
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