Ryanair has called an Extraordinary General Meeting of Aer Lingus.
The airline has issued a notice of requisition under the Companies Act and Aer Lingus's Articles of Association.
The airline, which holds a 29.4% shareholding, had asked Aer Lingus for the EGM, but Aer Lingus rejected the call on Friday.
Ryanair Chief Executive Michael O'Leary claimed that the directors of Aer Lingus were in breach of their statutory duty in failing to call the EGM.
He said they could find themselves personally liable for that failure.
Aer Lingus acknowleged that it had received the latest Ryanair letter and said it would respond in due course.
Ryanair is proposing that shareholders discuss a resolution calling for Aer Lingus to maintain its Shannon-Heathrow service and explore the €4m a year of additional cost reductions recently identified by the Shannon Airport Authority.
Aer Lingus had said on Friday that the holding of an EGM would infringe Irish and EU competition law.
The chairman of Aer Lingus, John Sharman, said Ryanair's proposed resolutions were clearly self-serving and were motivated by their own commercial interests.
Mr Sharman said the Aer Lingus board had also received legal advice that said it would be in breach of its fiduciary duties to call an EGM to consider the proposed resolutions.
Meanwhile, there has been widespread condemnation of the Taoiseach's statement last night that the Government will not be intervening to force Aer Lingus to reverse its decision.
The Shannon Action Group, which represents Aer Lingus workers, again called on Fianna Fail TDs and Ministers in the mid-west to support the demands for an EGM and to vote against the Government in the Dáil.
The group says the Government is totally failing in its commitments to the region.
And in Ennis last night, a Fianna Fáil Cumann passed a vote of no confidence in the Taoiseach for his handling of the Shannon affair.
It said he was failing to provide political leadership and was also failing to protect the economic fabric of the west.
