A prototype of the 'unsend' feature was spotted by Jane Wong, who shared screenshots on Twitter with a message explaining that it is now available "for everyone".
However, it appears to still not be fully rolled out for all Messenger users, with only the 'delete message' option available when tested by The Independent. Deleting messages in this way only removes them from the person's inbox who deleted them.
Mr Zuckerberg and other senior Facebook executives have been able to use an unsend feature for several years, according to an April report from TechCrunch.
Its introduction came as a result of the Sony Pictures hack in 2014, during which personal information of Sony employees was compromised.
"After Sony Pictures' emails were hacked in 2014 we made a number of changes to protect our executives' communications," Facebook said at the time.
"These included limiting the retention period for Mark's messages in Messenger. We did so in full compliance with our legal obligations to preserve messages."
Other apps with messaging functionality, including Snapchat and Facebook-owned Instagram, already allow users to unsend messages on their platforms.
A Facebook spokesperson was not immediately available for comment but the firm told TechCrunch that it is working on developing the feature.
"Facebook internally tests products and features before they ship to the public so we can ensure the quality of the experience," the spokesperson said.
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