Communication Workers Union (CWU) national official Andy Furey said: "Our members have sent a strong message to Post Office management today by solidly supporting strike action against closures, job losses, and pay.
"We hope the Post Office listens to the concerns of their staff. They can avoid further disruption by agreeing to negotiations to resolve this dispute.
"It's ironic that the Post Office has been trying to say offices remained open today when by their own plans they want to lose 76 Crown offices. That's 20% of the network and would hit communities badly.
"We won't let these go without a fight and ask again for the Post Office to meet us to resolve this. We're confident there is a way forward but this has to be by negotiation."
More top news
The Republican presidential candidate's Hollywood Walk of Fame star has been vandalised again.
Ukip has "formally reprimanded" Mike Hookem over a scuffle with colleague Steven Woolfe which landed the latter in hospital.
Popular cleaning products promoted as being fine to be flushed doing the toilet are being blamed for clogging drains and causing floods.