Transport stoppages planned for next Monday were called off yesterday by unions in response to an invitation to talks by the Minister for Transport, Mr Brennan.
The unions concerned, however, have restated their opposition to the Minister's plans for public transport.
In a letter to Mr Brennan, SIPTU and the National Bus and Rail Union (NBRU) disputed his assertion that there was a "very strong measure of agreement" between them.
"It cannot be said that there is any measure of agreement between us, let alone a very strong measure as stated in your letter," they wrote in a joint letter from Mr Noel Dowling of SIPTU and Mr Liam Tobin of the NBRU.
Mr Brennan had made the claim in a letter to the unions on Monday inviting them to talks. In a statement yesterday, the unions said they would attend a meeting, which is to take place on February 4th.
They said it was "regrettable", however, that they had "had to mobilise members on such a grand scale to secure the right to be consulted properly on change".
Thousands of bus and rail workers staged a four-hour stoppage and held rallies last week to protest at Mr Brennan's plans to break up CIÉ and introduce competition to the sector.
A similar demonstration had been planned for next Monday, before the Minister's invitation to talks.
In his letter to the unions, Mr Brennan said his aim was "simply to deliver to the general public a more efficient, reliable and competitive transport service".
In their reply, Mr Dowling and Mr Tobin said the Minister's approach would, "in fact reduce the level of service and quality of public transport".
They also asked Mr Brennan for "immediate information" on how many licences had been issued to private operators, including those that had yet to be activated.