Air New Zealand said in a statement that Flight NZ289 from Auckland to Shanghai was over four hours into its journey Sunday when it returned to Auckland after it was discovered a "technicality" meant the plane wasn't registered in China.
When asked to comment on the matter during a press conference on Monday, China's foreign ministry spokeswoman Hua Chunying said the plane was "improperly temporarily deployed, failed to obtain destination permission, and took the independent decision to return while in flight".
Ties with China have been tense under Ardern's government which has openly raised concerns about Beijing's growing influence in the South Pacific, and rejected Chinese telecoms giant Huawei's first local bid to build a 5G mobile network.
But on Tuesday it was reported that China was angry about a reference to Taiwan in some paperwork. According to sources "the Chinese were very explicit" about what the issue was, however the issue was not resolved.
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The unorthodox incident has prompted speculation the issue with the plane's paperwork was due to an error in the airline referring to the city of Taipei as the capital of Taiwan rather than a city in China.
An worldwide flight from Auckland to Shanghai has turned around mid-air and returned to New Zealand, sparking concerns over increasingly frosty relations between the two countries and setting off a political war of words.
"We've got a situation right now where the Prime Minister is seeking meetings in China and she can't get them and there is a relationship problem here, " he continued.
Ardern's plans to visit Beijing past year were also put on hold due to scheduling problems, with her office saying in late November it was "difficult to find a time that suits everyone".
The same flight, NZ289, was turned back on a flight to China on Aug 24 previous year, although an airline spokeswoman said that was due to an engineering issue, not a permitting one.
Relations between the two countries have become increasingly strained in recent months, following a recommendation from New Zealand's spy agency that the roll-out of 5G by Huawei posed "significant national security risks". Air New Zealand announced in February past year it would begin flying between Auckland and Taiwan's capital city Taipei from November 1.