The Aer Lingus board has rejected a request by major shareholder and rival Ryanair to hold an EGM over the decision to drop the Shannon to Heathrow route.
The airline said the resolutions put forward by the low-cost carrier's chief executive would result in a breach of European Union and Irish competition law.
Aer Lingus chairman John Sharman, said it was a self-serving attempt by Ryanair to exert influence over the airline.
"Ryanair's recent takeover bid in which it sought to acquire control of Aer Lingus was prohibited by the EU Commission on competition grounds. It is now seeking to circumvent this decision by exerting influence on Aer Lingus through its minority shareholding," Mr Sharman said.
"As recently as June, Ryanair was ready to give up Aer Lingus Heathrow slots in an attempt to acquire control of Aer Lingus. Its recently expressed concern in relation to these slots therefore has no credibility."
A Ryanair spokeswoman said: "We have no comment to make until we receive a reponse to our request to Aer Lingus."
Ryanair - which has a 29 per cent stake in Aer Lingus - believes it can force an EGM as a major shareholder. It is understood that Ryanair bosses are now considering whether or not to go down that route.
The Atlantic Connectivity Alliance lobby group, set up after Aer Lingus decided to drop the Shannon routes to Heathrow, said it noted the Aer Lingus decision and said in a statement: "The decision does not impact on the campaign being taken by ACA to retain the Shannon Heathrow slots and preserve them in perpetuity for Shannon.
"The ACA campaign will continue across a number of strands, including meeting with Transport Minister, Mr Noel Dempsey TD in Dublin next Wednesday."
It emerged earlier this week that the Government has been advised by Attorney General Paul Gallagher SC that a majority vote by Aer Lingus shareholders in favour of the retention of the Shannon-Heathrow air route at an egm would not be enough to save the service.
Ministers who discussed the controversial decision to abandon the route at the first Cabinet meeting since the summer break on Wednesday were told that, ultimately, the power to reverse the decision rests with Aer Lingus management and not the shareholders.
After the three-hour meeting, Minister for Transport Noel Dempsey said while he was deeply disappointed at the Aer Lingus decision it must be accepted that it will not be changed and the focus now needs to be on finding an alternative before next January.
Mr Dempsey said he acknowledged the move will affect the region but stood by his earlier comments that there had been exaggeration with "scary" statements being made such as a claim that 100,000 jobs could be lost.
Asked did his comments about exaggeration apply to his Cabinet colleague, Minister for Defence Willie O'Dea, who had said the pull-out represented an "Armageddon situation", Mr Dempsey said: "The same answer applies."