Unions and the Department of Transport failed to make progress yesterday after nearly eight hours of talks on the future of CIÉ.
The two sides are to return to the negotiating table today, however, in the hope that common ground can be found on plans by the Minister for Transport, Mr Brennan, to reform public transport.
They have set aside five days for intensive discussions aimed at resolving the row which has led to sporadic disruptions of public transport over the past 18 months.
Mr Liam Tobin, general secretary of the National Bus and Rail Union, said Department officials had presented a paper to the unions at yesterday's talks.
The proposals outlined had been "totally rejected", but the two sides would continue with their efforts to reach agreement, he said.
The talks, which are due to continue until Tuesday, are being chaired by Mr Kevin Foley of the Labour Relations Commission.
The most contentious issue is the manner in which increased competition by private operators should be introduced to the Dublin bus market.
Unions insist that Dublin Bus should be allowed to maintain existing operations and compete for new routes.
Initial plans outlined by Mr Brennan in late 2002 would have seen Dublin Bus surrender 25 per cent of its services to private operators by the beginning of this year.
