The second phase of the union action will see 24-hour walkouts today, Friday and Saturday.
More strike action could follow as Billy Hayes, general secretary of the CWU told the BBC: “I can see the strike action increasing now.”
Union chiefs and Royal Mail bosses were close to agreement on Tuesday evening, but the CWU reportedly issued fresh demands on Wednesday morning, which were not resolved before strike action was called.
Royal Mail Letters managing director, Mark Higson, told the BBC his focus would now move to minimising the disruption to customers during the three-day walkout.
The CWU has said it will take legal action against the Royal Mail over the decision to take on 30,000 temporary staff to deal with the Christmas period and the backlog created by strike action.
Retailers including John Lewis, eBay, and Argos have said they will use alternative delivery services to avoid the disruption caused by the strikes in the run up to Christmas.