Heathrow this week demanded airlines stop selling some tickets for summer flights, limiting the number of passengers flying from the hub to 100,000 per day.
Emirates said Heathrow had given the airline 36 hours from Wednesday to reduce capacity on its six daily flights, which are operated with the Airbus A380 superjumbo.
The airline said tens of thousands of passengers would be affected if the airline did reduce capacity and that it was impossible to rebook travellers as upcoming flights were full.
A spokesperson for Emirates said: “Their communications not only dictated the specific flights on which we should throw out paying passengers, but also threatened legal action for non-compliance.
“Until further notice, Emirates plans to operate as scheduled to and from Heathrow.”
The airline accused Heathrow of “incompetence” and of having a “blatant disregard” for passengers while urging the airport’s shareholders to scrutinise decisions being made by its management team.
Emirates said dnata, a unit of parent Emirates Group that provides ground handling and catering services at Heathrow, was capable and ready to handle its flights there.
“So the crux of the issue lies with the central services and systems which are the responsibility of the airport operator.”
A Heathrow spokesperson said the airport had been forced to impose restrictions to help ease the pressure of staff shortages.
“We had no choice but to take the difficult decision to impose a capacity cap designed to give passengers a better, more reliable journey and to keep everyone working at the airport safe,” a statement said.
“It would be disappointing if instead of working together, any airline would want to put profit ahead of a safe and reliable passenger journey.”
IATA has criticised the cuts.
