Members of the Communication Workers Union were due to walk out on Monday for the 13th time since Easter in a row over pay and the future of Crown offices - the larger branches usually sited on high streets.
The union said it had decided not to go ahead with the industrial action after Post Office chief executive Paula Vennells pledged to hold a series of intensive talks next week to reach a settlement.
CWU official Andy Furey said: "In her letter, Paula Vennells commits to authorising whatever resource is needed to evaluate areas where we can move towards concluding an agreement.
"After seven months and 12 rounds of industrial action we are pleased the Post Office is finally accepting responsibility for this dispute and coming to the table with serious intentions to find a resolution once and for all."
The union said staff in the country's 372 Crown offices have not had a pay rise since April 2011, and faced an uncertain future because of plans to close or franchise over 70 of the branches.
The move could lead to the loss of 1,200 jobs, the CWU warned.
Unite said its members had not received a pay rise since June 2011.
A Post Office spokesman said: "The Post Office and CWU teams met all day Tuesday and Wednesday this week to talk about our vision for the future of the Crown network. These talks have been constructive, which is welcome, and we will be continuing these talks next week.
"While neither of us underestimates the work still to do, the Post Office and the CWU remain committed to resolving the present dispute and we have confirmed meetings for next week to continue to work towards this.
"In light of this, the CWU has decided to call off the strike action for next Monday so we can continue our discussions. The Post Office welcomes this decision, which is good news for our customers and will allow us to focus on the ongoing discussions."
Unite said the strike by managers in Crown offices will go ahead on Monday as planned.
An official said insufficient progress had been made in efforts to resolve the pay dispute.
© 2013 Press Association