The files were uploaded to file-sharing sites and the Bit Torrent file-sharing network, and links to them were posted in a message that claimed to be from the same hacking group behind the Sony attack.
"We have already given our clear demand to the management team of Sony, however, they have refused to accept," said the message pointing to the files. "We are sending you our warning again."
The hackers said the email boxes belong to Steve Mosko, president of Sony Pictures Television, and Amy Pascal, co-chairman of Sony Pictures Entertainment.
The Microsoft Outlook mailbox files run to several gigabytes and apparently contain thousands of messages sent to and by both executives over several months.
A handful of the emails, seen by IDG News Service, appear to include discussions between company executives, lists of phone messages that include contact details for executives at other companies, business information, and personal messages to family members.
In one file, the most recent messages point to the email box being copied on the evening of Nov. 22. Sony first learned of the hack on November 24, when computer screens at the company showed a message telling users the network had been hacked.
The release of the email files is another blow to Sony Pictures, which is still attempting to determine who was responsible for the attack on its network. The company has been quiet on the investigation since it launched two weeks ago. Private computer security companies and the U.S. Federal Bureau of Investigations are understood to be spearheading the probe.
An initial leak of corporate data soon after the hack revealed thousands of files stolen from company servers. They included confidential business information, the salaries of Sony Pictures employees, staff medical records and computer passwords.
The company did not immediately respond to a request for comment.
Martyn Williams covers mobile telecoms, Silicon Valley and general technology breaking news for The IDG News Service. Follow Martyn on Twitter at @martyn_williams. Martyn's e-mail address is martyn_williams@idg.com