New Zealand prime minister Jacinda Ardern has told journalists she "sensed an interest" from US president Donald Trump in gun buybacks during their meeting in New York.

The pair of leaders held their first formal meeting on Tuesday, alongside the UN Climate Action summit.

Ms Ardern didn't leave the 25-minute meeting with any new announcements or agreements.

The prime minister did say a discussion of the Christchurch mosque terrorist attack led to New Zealand's response to the tragedy.

"It was a conversation around our buyback and obviously the work that we had done to remove military style semi-automatic weapons and assault rifles and so we had a conversation around what had happened in New Zealand and how it worked," she said.

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In the wake of the attack, Ms Ardern has led an international coalition to eliminate extremist content on the internet, labelled the 'Christchurch Call'.

The United States is not a signatory, citing freedom of expression commitments in the country's constitution.

The United States has a horrific record on gun safety, with more mass shootings than anywhere else in the world, including schools.

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While other countries that have suffered mass shootings - such as Australia and New Zealand - have implemented more restrictive gun ownership regimes, politicians in the United States are deadlocked on how to prevent the killings.

A United States diplomatic "readout" of the meeting said the president expressed the country's "steadfast support" for New Zealand after the attack.

The readout, issued by the White House press office, said the leaders also discussed defence and security, and trade.

AAP

Reports from travelling New Zealand journalists said the pair also touched on climate change - despite wildly different views and policies in the area.

Ms Ardern said the US president "holds New Zealanders in very high regard", with a possibility of new trade negotiations to come.

"I think actually the knowledge that the president already has of New Zealand, the warmth and high regard in which he clearly holds New Zealanders and the place, was really clear and that's a good starting point for any conversation," she said.

"The idea of continuing a conversation around New Zealand's trade relationship with the United States was greeted warmly and I expect there will be some ongoing conversations."

While Mr Trump has flagged a potential visit to Australia at the end of 2019, a presidential visit to New Zealand is unlikely until Auckland hosts the 2021 APEC summit.