The newborn was named Harper.
The father is accused of bringing Harper into the woods and covering her in snow before shooting her.
Her body was found five days later with a gunshot wound to the head.
It is believed Kruckenberg-Anderson initially told police he had given his baby to a friend, but was unable to give police the friend's name or contact details.
Kruckenberg-Anderson claimed he met the friend through SnapChat and would give the friend money in return for taking his daughter to an adoption agency.
He then led police to Harper's body and said he left the newborn to die of exposure, telling police she cried as he walked away , NBC 15 reported.
This " caused him to emotionally break down, fall to his knees and cry".
However, the local medical examiner's office discovered a bullet hole in the child and a casing nearby.
In a follow-up email, Kruckenberg-Anderson admitted shooting the newborn in the head.
A judge handed down a US$1 million bond at his court appearance earlier this week. He will return to court later this month.
Where to get help:
• 0800 543 354 (0800 LIFELINE) or free text 4357 (HELP) (available 24/7)
• https://www.lifeline.org.nz/services/suicide-crisis-helpline
• YOUTHLINE: 0800 376 633
• NEED TO TALK? Free call or text 1737 (available 24/7)
• KIDSLINE: 0800 543 754 (available 24/7)
• WHATSUP: 0800 942 8787 (1pm to 11pm)
• DEPRESSION HELPLINE: 0800 111 757 or TEXT 4202
• NATIONAL ANXIETY 24 HR HELPLINE: 0800 269 4389
If it is an emergency and you feel like you or someone else is at risk, call 111.
