The main postal workers' union is writing to Royal Mail to call for fresh talks in an attempt to avoid the first national strike in more than a decade.
Royal Mail says it cannot afford a bigger pay offer
The Communication Workers Union says it wants further negotiations after its members turned down a 2.5% pay rise and voted in favour of industrial action.
Its call comes as it is expected to set dates later this week for a series of UK-wide stoppages.
A Royal Mail spokesman said it was always willing to meet with the union.
The Communication Workers Union (CWU) wants an improved pay offer, and for Royal Mail to rethink its modernisation plans, which the union claims will cost 40,000 jobs.
About 77% of Royal Mail's CWU members voted for the strike action.
"We will set out our case for a pay rise which matches inflation," said a CWU spokesman.
"We also want a deal on modernisation which has the acceptance of workers.
"We will ask the Royal Mail to step back from their current cost-cutting frenzy."
Royal Mail has said it cannot afford any more than the 2.5% pay rise it has offered.