A public transport strike looked likely to be averted last night after the National Bus and Rail Union welcomed an offer of talks from the Minister for Transport, Mr Brennan, who said he was open to new proposals.
The other main CIÉ union, SIPTU, meets today to consider its response to a letter sent to the unions yesterday on Mr Brennan's behalf.
Train services to and from Westport, Co Mayo, meanwhile, face the threat of further disruption today.
In yesterday's letter to the unions, the Department of Transport secretary general, Ms Julie O'Neill, said Mr Brennan was open to new proposals about the future transport needs of Dublin.
She emphasised, however, that the Minister remained "firmly of the view" that franchising out routes was the best way of opening the market to new entrants.
The letter was given a "cautious welcome" by the NBRU general secretary, Mr Liam Tobin, who said his union would do everything it could to make talks work.
"We particularly welcome the fact that he has accepted for the first time the need to open his mind to different ways of achieving the same objectives for improving the public transport system," he said.
SIPTU's national industrial secretary, Mr Michael Halpenny, said the union would issue a considered response after a meeting today of its CIÉ strike committee.
In her letter, Ms O'Neill said unions had already accepted the objective of "regulated market opening" in bus transport, through their participation in the public transport partnership forum.
Mr Brennan believed this objective could be achieved without undermining the terms and conditions of Dublin Bus employees.
As Mr Brennan had stated to the unions in a meeting last Monday, he was "firmly of the view that franchising is the most effective means of achieving genuine market opening to new entrants.
"However, he remains open to additional suggestions provided they are directed at achieving the same objective."
The Minister was also open to "reasonable proposals" relating to the pace of the introduction of competition, she said.
Mr Brennan was proposing intensive discussions within a tight timeframe and under an independent chair.
Mr Tobin said the Minister had at last accepted the validity of the public transport partnership forum of 2002. "If he had been prepared to use this as the basis for discussions we may well have resolved our differences long ago," he said.
However, it was better late than never, and the NBRU looked forward to participating fully in the new process.
If SIPTU adopts a similar stance today, a series of rail and bus stoppages will be put on hold for the time being at least.