The Communication Workers Union (CWU) set a four-week deadline for breaking the deadlock or it will launch a ballot for industrial action.
A timetable for stoppages was set, raising the threat of nationwide walkouts for the first time since 1996.
The stakes were raised when the union announced that a huge majority of its members opposed the idea of shares being given to workers.
There are suggestions that a scheme, under which workers could receive up to £5,000 in shares, could be announced within the next few weeks. The Department of Trade and Industry has insisted no decision had yet been taken.
A consultative ballot showed that 90,103 union members supported the CWU's vision of a publicly owned Royal Mail - a majority of 98.5%.
A separate ballot of 1,000 CWU members, run by an independent company, showed that 949 backed the union.
Within minutes of the announcement, the Royal Mail revealed that it had asked an independent auditor to examine the union's ballot as well as one held by the company.
Royal Mail chairman Allan Leighton said that 80,000 workers supported his idea for issuing shares.
"Royal Mail has asked an independent auditor to examine the process of both consultations. We assume the union will be able to provide the auditor with the names and work numbers of all those who voted, as we will be doing."
The CWU's general secretary, Billy Hayes, said Mr Leighton had a "bloody cheek" asking an auditor to examine the ballot, adding: "We will not take lessons from him on how to conduct a ballot."
Union officials said they had no intention of co-operating with the move.
The union's annual conference in Bournemouth agreed an emergency motion calling on Royal Mail to reopen pay talks following the imposition of a 2.9% rise.
Mr Hayes said: "The message that goes out from here today is that democracy has been restored to the Post Office.
Deputy general secretary Dave Ward said the Royal Mail had made a "huge mistake by imposing the pay deal and banning the union from holding its ballot in the workplace".
He accused Mr Leighton of putting forward the shares idea without having any authority to do so: "Imposing pay is not a sign of strength, it is a sign of weakness. The Royal Mail wants this union out of the way so it can drive through its business plan without any negotiations.
"The Royal Mail believes our people will be conned into accepting everything they want to introduce purely on the basis of some phoney shares."
The dispute involves around 150,000 Royal Mail workers. A separate row is brewing among 6,000 Post Office workers after the union rejected a "final offer" of 2.9%.
