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."