Warrant Officer Brett Pene said the haka referred to current New Zealand soldiers being descendants of those who fought various campaigns around the world.
After a demonstration, the haka instruction took place behind closed doors.
It's believed the Prince was given a video of the haka earlier this week to help him prepare.
Mr Pene said the royal had done well given the time he had to practice.
He said it was humbling and appropriate for the Prince to join in, given Prince Harry was also in the army.
Prince Harry was clearly given a thorough workout while practising - he ended the haka red and sweating.
Image 1 of 9: Prince Harry performing a haka with 1 Brigade soldiers during his visit to the Linton Military Camp near Palmerston North. 13 May 2015. Photo / Mark Mitchell
It had been a rigorous 20 minutes, Pene said.
"Yeah, he was sweating, we were sweating, a bit of frustration set in."
The prince had also shown a lot of interest in the background and meaning of the haka, Mr Pene said.
Prince Harry was welcomed into the Officer's Mess, where the hangi of chicken, pork, lamb and veges was served, with a karakia (prayer).
He chatted to members of the Defence Force, including wounded soldiers, families of the fallen and Invictus Games athletes. He looked at ease and interested in what people had to say.
— Governor-General NZ (@GovGeneralNZ) May 13, 2015
Harry was reunited with wheelchair-bound wounded warrior Corporal Jason Sturley, 47, of Linton, who had met the prince before and watched him try a game of wheelchair rugby at last year's Invictus Games.
— Governor-General NZ (@GovGeneralNZ) May 13, 2015
Jason says: "He was seeing how we were doing for the Invictus Games. He's a fantastic guy. Down to earth. Very genuine. We had a bit of banter. We joked about wheelchair rugby. He's had a go at it. He competed. He said everyone treated him like anyone else out there."
Jason was injured in a 2007 deployment in the Solomon Islands. He lost a leg due to septicaemia.
"You grow up dreaming of meeting a prince, so I was really nervous, but he was awesome," she said.
After his hangi lunch, Prince Harry dropped by the Nursing Corp, which is celebrating its 100th anniversary, to deliver a message from its patron, the Princess Royal.
In the first group, he recognised a woman he met in Italy for the 100th anniversary of Cassino last year.
"That was when we took the veterans to Cassino," Lieutenant Sarah Linehan, 43, of Hastings, said afterwards. "I remember how lovely he was with the veterans."
She complimented him on his military badge with a kiwi on it.
Harry also chatted about Afghanistan to Major Simon Ainsworth, 38, of Linton, who'd been to Afghanistan three times.
"We were at Afghanistan at the same time, relatively close," Major Ainsworth said. "We never crossed paths, but there's always awareness when high-profile people are on the ground. We were comparing stories."
Lieutenant Nikki Houlahan, 29, of Linton, also talked to Harry.
"He asked how we celebrated our centenary," she said. ""We said we were well behaved, which got a giggle."
The Prince, who holds the ranking of captain in the British Army, touched down in an an New Zealand Defence Force NH90 chopper. He was then asked to drive a Polaris All Terrain Vehicle across the base.
He was happy to rip it up behind the wheel of the NZ Army ATV but his British conditioning meant he baulked when it came to driving on the grass.
Staff Sergeant Jason Edgecomb was in the passenger's seat and said the Prince got used to the vehicle quickly and while there were no donuts, he had "put his foot down".
"He took it nice and slow round for the media and from there he put his foot down in the areas he could. He said he enjoyed it and I think the grin on his face coming in was probably the answer."
However, when told to drive along a nicely mowed grass area at the end the Prince had baulked, saying he kept waiting to be told off. Mr Edgecomb put that down to his British upbringing.
"There was a bit of a British [thing], not used to walking on the grass, not allowed on the grass so obviously here we are allowed to put the vehicle over the grass."
He said the ATVs were not designed for tarsealed roads and were driven on grass where possible.
He said Prince Harry also got points for safety, driving with two hands on the wheel as the army tried to teach its young drivers to do. The Prince had also slowed down to drive through the forest, where soldiers were training.
Wearing the British Army uniform and a blue beret, he donned a helmet and pulled on a New Zealand military jacket, driving the vehicle to the base's hangi pits.
— Governor-General NZ (@GovGeneralNZ) May 12, 2015
Director Nigel Laughton spoke to Harry about the programme before the team posed for a group shot with the young royal.
Harry was then escorted outside, where residents were waiting in a workshop with wooden tables they have been building.
The prince, dressed in a dark polar fleece jersey over a light blue shirt, rolled up his sleeves up to help stain wood tables. He spoke to resident Zeb King who said he was an artist.
Harry asked if he had any pictures with him. Zeb handed him one of his son.
Seeing him today, she thought he hadn't changed much.
"He's just a lovely man."
McBratney took the day off work to stake out a spot in Cashel Mall with old photos, hoping that Harry would recognise her.
Prince Harry also visited a very soggy University of Canterbury campus to cheers from hundreds of students who braved thunderstorms and hail to catch a glimpse of royalty.
He met with masses of excited royal fans lining the streets of Cashel Mall, shaking hands, gushing over babies and posing for pictures.
May 13: Palmerston North • Visiting Linton Military Camp. He is to be taught the Army's haka.
May 14: Wanganui • Powhiri at Putiki Marae followed by a waka experience. • Meeting with veterans and a walkabout.
May 15: Auckland • Visit to Southern Cross Campus School where he will view a cultural performance and meet with students. • Visit to spinal rehabilitation unit. • Visit to Turn your Life Around. • Visit to Government House. There will be an evening reception to recognise emergency services.
May 16: Auckland • FIFA U20 event, followed by a walkabout at The Cloud. • Visit to High Performance Sport New Zealand at Mairangi Bay.