A spokesperson for Prime Minister Luxon said a letter had been received, and would be responded to, but added that it wouldn't be helpful to offer a running commentary on the two governments' communications.
A diplomatic row broke out between the two countries after the Cook Islands leader, Mark Brown, flew to Beijing two weeks ago to sign several agreements with the Chinese government.
Cooperation on seabed mining, the establishment of diplomatic missions and preferential treatment in regional and multi-lateral forums were some of the standouts in the agreement.
The coalition government is still analysing the documents and what, if any impact, they might have for national and regional security in New Zealand.
Foreign Minister Winston Peters and Luxon have both criticised Brown for not sharing the agreements with China ahead of the signing - an expectation they say should have been met under the 2001 Joint Centenary Declaration.
Brown has previously said New Zealand did not consult the Cook Islands on its comprehensive strategic partnership with China in 2014, which they should have done if the Cook Islands had a requirement to do so.
Peters is in Beijing this week, and is expected to raise New Zealand's concerns about the deal with his counterpart in a bilateral meeting this evening.
