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The issues affected people accessing Facebook and Facebook-owned Instagram and Messenger from about 6am today (NZ time).
Other users had been able to get into Facebook, but couldn't post or reply to anyone.
Facebook responded to concerns this morning, saying that some users may encounter challenges accessing the site as it was down for "required maintenance".
Downdetector.com, a site that monitors site outages, said the Facebook problem also affected parts of the United States including the East and West Coast as well as parts of Europe and elsewhere, AP reports.
Facebook did not say what was causing the problem.
Via its Twitter account, Facebook said the outage was not due to a "distributed denial of service" or DDoS attack, a type of attack that hackers use to interrupt service to a site.
Social media users took to Twitter to express their frustrations - and to mock Facebook.
Among those having a bit of fun at Facebook's expense were Canterbury Police, who issued a tongue-in-cheek tweet reminding Kiwis not to report the issue to any of its departments.
Yesterday users encountered a number of problems accessing Google's YouTube, Gmail and Google Drive services.