Chinese Foreign Minister Wang Yi was in New Zealand this week meeting Luxon, his counterpart Winston Peters and trade minister Todd McClay.
Peters told reporters on Tuesday that he, Luxon and McClay have been invited to travel to China.
Dates for the visits have not been confirmed, a government spokesperson told AFP.
It would be Luxon's first visit to China since being elected prime minister last October.
New Zealand is part of the Five Eyes intelligence-sharing alliance alongside the United States, Canada, the United Kingdom and Australia.
But Wellington has been criticised for taking a softer line on China -- putting its trading relationship ahead of its allies' security concerns.
China has praised New Zealand's stance as "rational and mature", but has raised questions about security cooperation between New Zealand and Western allies.
Peters said Wang brought up the possibility of New Zealand joining the AUKUS alliance, a landmark pact aimed at counterbalancing China's rise in the Pacific.
"He did raise AUKUS with me and I pointed out the right of countries to organise their defence arrangements if they felt the need to have such arrangements," Peters added, without giving details.
"It was a very frank, candid and open conversation in that context. We understood where he's coming from. I'm certain he understands where we're coming from."
AUKUS is a pact between the United States, Australia and the United Kingdom to cooperate on the development of advanced weapons systems.
China has been fiercely critical of AUKUS' plans to supply Australia with a fleet of nuclear-powered submarines.
New Zealand's staunch anti-nuclear policy, adopted in the 1980s, means it would only be involved in "pillar two" of the accord, covering cyber warfare, artificial intelligence and the development of long-range hypersonic missiles.
China's FM Wang begins diplomatic blitz in New Zealand
Wellington (AFP) Mar 18, 2024 -
Chinese Foreign Minister Wang Yi made a rare visit to New Zealand on Monday, stressing the need to work with "friends" in the face of the "tumultuous international situation".
The trip marks the start of a diplomatic blitz through New Zealand and Australia, Wang's first visit to either country since 2017.
The whistlestop tour is expected to focus heavily on trade as Beijing looks to lessen the pain from slowing economic growth at home.
Speaking in the capital Wellington before a meeting with his New Zealand counterpart, Wang said the trip was also a chance to shore up diplomatic ties that have come under strain as Beijing adopts an increasingly aggressive stance on issues such as Taiwan and the South China Sea.
"In the face of the current tumultuous international situation, we are willing to strengthen strategic communication with our friends in New Zealand on international and regional issues of common concern," Wang said.
"And we will work together to maintain peace and stability in the region and the world," he added before his closed-door meeting with New Zealand Foreign Minister Winston Peters.
New Zealand is part of the Five Eyes intelligence-sharing alliance alongside the United States, Canada, the United Kingdom and Australia.
But Wellington has been criticised for taking a softer line on China -- putting its trading relationship ahead of its allies' security concerns.
In a statement on Monday, Peters said the talks touched on "trade, business, and people-to-people links", but also acknowledged "areas of difference such as human rights".
"We also highlighted New Zealand and China's shared interest in a secure and prosperous Indo-Pacific region and raised concerns over increased tensions in the South China Sea and Taiwan Strait," he added.
China is New Zealand's largest trading partner, and Chinese consumers have long had an appetite for the country's meat, wine, milk and wood.
Wang said he believed that "China-New Zealand relations will continue to be at the forefront of China's relations with developed countries".
"The relationship between us has developed smoothly and well," he said.
Later this week, Wang will meet Australian Foreign Minister Penny Wong in Canberra.
China and Australia have recently resolved a series of simmering trade disputes that saw Beijing impose tariffs and trade barriers on key exports in 2020, retaliating after Canberra barred Huawei from 5G contracts and called for a probe into the origins of Covid-19.
But the two nations continue to spar over human rights and Beijing's growing clout in the Pacific region.
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