Fresh strikes over the future of Post Offices are set to be called unless a row over closures, jobs and pay is resolved.
Members of the Communication Workers Union in Crown offices - the larger branches usually situated in high streets - walked out on Saturday in protest at plans to close or franchise 70 sites, as well as over pay.
The Post Office said over 100 branches were open despite the strike and accused the union of ignoring the "harsh commercial realities" it faced.
Andy Furey, CWU national official, said there had been no moves to arrange peace talks since the strike.
He said: "The strike action was overwhelmingly supported and all indications are that we can sustain the support and build on the solid action of this weekend.
"We have a meeting of our Post Office reps on Wednesday and if there is no movement from the Post Office management we would expect to be serving notice later this week for further strike action.
"With a vote of almost 9 to 1 in favour of strike action, the Post Office is seriously out of touch with its staff on these issues.
"We will not be walking away from this - it's far too important in terms of jobs, services and the future of the Post Office. We hope management realise this sooner rather than later and agree to meaningful negotiations to avoid further disruption."
The Post Office said its Crown branches were losing £40 million a year, adding: "The Post Office is transforming its network to improve customer experience and in turn bring in new business.
"We are committed to the Post Office remaining a key part of UK high streets and our plans ensure this will happen. This means for 70 of our Crown branches - less than 1% of our network - we will be looking to partner with a suitable retailer, whilst at the same time we will invest £70 million in the remaining 300 Crown branches to modernise and grow services to ensure their long-term viability."