Wellington says the Cook Islands must take concrete steps to "repair" their relationship.
The recent spree of deals between the two is upsetting traditional allies wary of Beijing.
Wellington says it was not properly consulted over the agreement, which is due to be signed this week.
Cook Islanders are citizens of New Zealand, which oversees the island's foreign affairs and defence.
People living in the Pacific nation are divided on whether to push ahead with deep-sea mining for polymetallic nodules.
Provides an overview of the Cook Islands, including key facts about this Pacific country.
An overview of the media in Cook Islands, including links to broadcasters and newspapers.
The Cook Islands' bowls team have been staying in Gloucestershire ahead of the Commonwealth Games.
The Pacific country fears the virus is now circulating there, despite a vaccination rate over 99%.
