As commemorations kicked off to mark the landing of the British explorer James Cook 250 years ago, New Zealand Prime Minister Jacinda Ardern on Saturday called for her country to have a more open conversation about its history.

Britain delivered a "statement of regret" to indigenous Maori earlier this week for the killing of nine of their number immediately after Cook's landing, although it did not offer a formal apology.

Descendants of some of those killed were in attendance at Saturday's events, beginning with the arrival of dignitaries and ships from around the Pacific.

"We have to now make sure ... that we have this conversation, that we talk about our history much more openly," Ardern said during live coverage of the events by broadcaster TVNZ1.

"We were only really telling, I believe, 50 percent of the story, and not always telling it well."

New Zealand should continue to learn and tell the full story of its past, she added.

"I'd ask anyone to imagine what it would be like to hear a story be retold, knowing that, actually, you lost an ancestor directly because of those encounters and not feeling like that'd be adequately told."