Prime Minister Jacinda Ardern has appeared on The Late Show with Stephen Colbert, offering the Lord of the Rings fan "citizenship of Hobbiton" and dodging a diplomatic incident in questions about US President Donald Trump.

Colbert - who is no fan of Trump - asked Ardern about Trump's handshake, saying he has heard some leaders had to develop special strategies to deal with it.

"I went in for a natural shake. I have a quite firm handshake, and I didn't particularly notice," Ardern said.

Colbert said he had noted her firm handshake and she replied "it's the way we shake in New Zealand".

That prompted Colbert to observe New Zealanders were "a very vital people - very vigorous".

"I don't think I've ever heard us described in that manner," Ardern said. "It makes us sound like a health product."

It earned her a good laugh from the audience and Colbert responded with the possible advertising plug: "fresh squeezed Kiwi".

Ardern was relaxed and enjoying her time - managing to get in a tourism plug by inviting Colbert to visit.

The trickiest moment came when Colbert asked Ardern about whether leaders had been laughing at Trump at the UN.

Laughter had interrupted his speech after he claimed his administration had done more than any other.

Ardern asked if Colbert was trying to cause a diplomatic incident, and said she herself was a simple observer of the laugh in question.

Stephen Colbert noted that Jacinda Ardern has a very firm handshake. Photo / CBS

She said a second laugh after Trump had said he was not expecting the first laugh had been laughing with him - but avoided commenting on the first laugh beyond saying it was "a spontaneous murmur".

"I observed."

Colbert is a fan of the Lord of the Rings - and asked Ardern if she was a Hobbit.

"I do find it slightly offensive that every New Zealander starred in either Lord of the Rings or The Hobbit," Ardern said, before admitting she had indeed auditioned but was not successful.

She said Hobbiton had contacted her to say Colbert could become a Citizen of Hobbiton: "you get a mug", she said.

"Come to New Zealand and we'll make the ceremony official. There's a direct flight from Chicago from November, so it's nice and easy."

Colbert also rubbed in the transtasman rivalry, asking whether Australia got an exemption to the steel tariffs imposed by Trump - and then whether New Zealand did.

Ardern had to admit New Zealand was still trying - she had raised it with Trump at a reception earlier that week, but said her partner had provided something of a distraction by knocking over a flag pole next to them.

She had not known if it was an American flag. "As I turned around he was holding what I can only describe as a long metal prong ... I'm surprised no one leapt on him at that point because it looked like a weapon."

There were cheers when Colbert introduced her as the youngest elected woman leader in the world, and coos when Colbert put up a photo of Ardern and Neve in the General Assembly.

Colbert began gently, asking Ardern about her time living in New York working in a soup kitchen.

As she ended her interview, he farewelled her with a "good luck with the tariffs and everything" and added a good luck for Ardern's own speech at the General Assembly the next day: "I hope everyone laughs."

Backstage, Ardern got to hang with other guests - actress Candice Bergen, who will again star in Murphy Brown as it returns.

Neve was there for the occasion, backstage with her mother while Clarke Gayford sat in the audience.

The show is filmed in the Ed Sullivan Theatre on Broadway, and the light show on the domed ceiling before Ardern came on featured kiwi and kiwifruit.

Colbert began the show with a lengthy roasting of Trump's press conference earlier that day.

It was the day before the hearing for Trump's Supreme Court nominee Judge Brett Kavanaugh, who has denied accusations of sexual harassment when he was at high school.

The filming of the show was delayed - which Colbert said was because of the length of Trump's press conference.

Colbert said that meant they had to constantly re-write his monologue. "So you're going to see some very fresh jokes."

In advance of her appearance on the show, Ardern responded to the Flight of the Conchords' plea for an invitation to come to dinner when they appeared on the same show two days ago.

Colbert got in some practice understanding the New Zealand accent by getting Flight of the Conchords stars Bret McKenzie and Jemaine Clement on the show two days ahead of Ardern. While on, they told him to ask Ardern if they could come to dinner.

Ardern replied today, saying they were more than welcome. "Open invitation. I'd welcome them for dinner if they picked me up from the airport."

Prior to the show, Ardern said she still had no idea what Colbert was going to ask, but she knew he was a massive Lord of the Rings fan.

"I imagine if you bring anyone in from New Zealand there is likely to be a discussion there."

The last time a New Zealand leader was on The Late Show was when John Key went on with then host David Letterman in 2009.

He was mocked for his efforts reading a list of 10 things about New Zealand - but Ardern said today she thought he had done pretty well. "He was pretty deadpan in his delivery. I thought it was quite a good try."

Before the filming, Ardern said she did not know how political the interview was likely to be. "My job is to be there to represent New Zealand well - both our values on the world stage but also as a destination."

Ardern was also asked by an American journalist how Neve had been received by the other world leaders.

"She comes to functions with me. Politicians love holding a baby, so..."