The Labour Party has urged the Minister for Transport, Mr Brennan, to accept a proposal from trade unions representing Aer Rianta workers to enter talks with them on the future of the company.
Ms Roisin Shortall, Labour Party spokeswoman on transport, has also urged unions not to engage in strike action until a compromise has been reached.
"Minister Brennan should accept the invitation from the Aer Rianta group of unions for discussions without preconditions on the future of the company in order to avert industrial action at the company," Ms Shorthall said.
"There are many critical issues posed by the Minister's announcement that he intends to abolish Aer Rianta, not least issues of competition, the status of the Eurobond of the company, the debt-free status of Cork and Shannon airports, cross-subsidisation, and the management contracts the company has with other companies."
Ms Shorthall's comments follow a meeting yesterday of unions opposed to the Government's plans to break up the company.
The five unions representing workers said they would shut down Dublin, Cork and Shannon airports to coincide with the start of Ireland's EU presidency next January in protest over the plans.
Protests are also likely to include smaller-scale work stoppages in the run-up to Christmas as well as major escalation designed to embarrass the Government when it takes over the EU presidency in the New Year.
The first two-hour work stoppage is to take place on Tuesday, November 4th.
However, the Minister intends to press ahead with his proposals to create three separate airport authorities, according to reports last night.
The Cabinet last week approved the heads of a bill to implement the proposals.