Talks were held again yesterday at the offices of the Trade Union Congress, which is acting as mediator in the dispute.
But talks ended without an agreement, descending into a war of words between both sides.
The two sides still cannot agree on the key efficiency-driven changes to working practices, including a clamp down on overtime, that Royal Mail wants to implement.
Royal Mail pointed the finger at the CWU and claimed there was a split in the union's ranks and that a hard-core London-based element of the CWU was blocking progress in negotiations.
The CWU for its part said it tabled a proposal yesterday morning and had to wait eight hours for a response. Its deputy general secretary, Dave Ward, told the BBC this morning that Royal Mail is "not telling the truth" about progress on talks.
Mark Higson, managing director of Royal Mail Letters, claimed the two parties had been "on the verge of a sensible agreement that would have allowed us to enter into in-depth discussions with the union over the future of Royal Mail in an atmosphere of calm".
"But just like last week the CWU leadership has failed to carry its own Postal Executive Committee, which appears to be split with London members at odds with the rest of the country and unable to reach any decision," he said.
An internal Royal Mail memo seen by ITV news outlined ways that the company would help postal workers do deliveries today, including hiding them in vans.
Royal Mail said that it expects the total volume of mail delayed by last week's strikes by the CWU to have fallen to around two million items by yesterday.
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