Nicole Leman died on Tuesday while climbing the Matukituki Waterfall.
Alaska Dispatch News has reported that the 24-year-old was the youngest daughter of former Lieutenant Governor Loren Leman.
He told the newspaper she was a happy and daring child and he was heartbroken at her lose.
She travelled to New Zealand to pursue her love of hiking and mountaineering.
"She wanted to climb in a beautiful area," he said. "It's beautiful here too, but she wanted to experience that in a different place.
"She is happy, somewhat daring and willing to do something most people just talk about doing. She would do a 10-day hike. Put everything she needed on her back and would just go."
Alaskan television network KTUU reported how New Zealand officials called Mr Leman and his wife, Carolyn, about the news late Tuesday night [US time].
The Leman family says Nicole had been enjoying the trip so much, she extended her stay in New Zealand by three months.
Loren Leman served as Alaska's eighth Lieutenant Governor from 2002 to 2006.
Her partner Kenton Curtis wrote a long, heartbreaking post on Facebook and added pictures that her family were yet to see from her time in New Zealand.
He wrote how he'd lost his closest friend and apologised to her family but reassured them that she died happy.
"I want you to know that she was having the time of her life in New Zealand, and had no regrets. She died in one of the prettiest places in the world, in a place we ourselves can only wish we could die."
However, he said he felt guilty as she had told him a dozen times that he was the biggest reason she came to New Zealand.
"I wanted her to take advantage of her post-college 20's, her independence, her freedom, and see the world that God made for us in person, one trail at a time. She made friends with everyone she crossed paths with. She stayed in more than 200 huts in New Zealand, and hit almost every single trail in both the North and South Islands. She was telling me how excited she was to come back, and how amazed she was that she only had a handful of trails in the entire country she hadn't done."
- NZ Herald
