A demerger would enable the two different businesses to focus on their "significant, but divergent" problems, it said.
A long-term strategy for the Post Office was also needed to reduce uncertainty, safeguard against further closures and build confidence in a sustainable post office network, chairman Nigel Stapleton said.
"Unless the government is able to provide a clear vision for the future, we are concerned the network will shrink further," he said.
However, Communication Workers Union general secretary Billy Hayes said separation would create greater uncertainty. "Royal Mail needs the Post Office to provide a universal service, while the Post Office remains dependent on Royal Mail for about a third of its revenue," he said.
Post offices could be subject to new performance-related contracts after a study by watchdog Consumer Focus revealed poor service and long queues at branches.