Rajeshwar Singh pleaded guilty to a charge of murder and two of breaching a protection order in the High Court in Wellington.
A police summary says Singh, a Fiji national, fell out with his wife 38-year-old wife Sarwan Lata Singh after their toddler died in 2011, Stuff.Co.Nz website reported.
The couple had married in Fiji and came to New Zealand in 1998.
They separated in November, but Singh continued to threaten and follow his wife to the point she slept with a knife under her pillow and meat cleaver under her bed.
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He was under a bail condition not to contact his wife or go to her house when he murdered her there on November 26.
In the early hours that day, Singh broke into her home and stabbed her to death.
He tried to hang himself in her garage afterwards, but police reached the spot before he died, Newstalk ZB reported.
He has been remanded in custody until sentencing on June 5, the reports said.