Additionally, if someone is placed under the Mental Health Act while in a police custody suite, they will be taken to a health facility within 30 minutes.
Police said the changes would ensure distressed people were assessed appropriately and in a preferred health setting.
They clarified that time caps applied unless there was an immediate risk to life or safety.
Northland and Central police districts are the last to apply the next wave of changes. Four Health NZ districts - Northland, Taranaki, Whanganui and MidCentral - will also make the shift on Monday.
Phase two was due to start between January and March, but was delayed in Northland to allow the region to be ready.
Police had not wanted to rush the process as they needed everyone to be confident in the changes and wanted to keep people safe.
Assistant Commissioner Mike Johnson said police were committed to the joint efforts that gave people access to appropriate and timely help.
“Police have always, and will always, respond when there is an immediate risk to life or safety.
“The change is about an increased health-led response, enabling our staff more time to get back into our communities to do the work that only police can.”
The major change in approach to mental health callouts has been criticised by those who worry that relevant services will not cope with the gaps created.
Mental health advocates called for the programme to be halted until either an alternative crisis response service or a larger mental health workforce was in place.
Karla Bergquist, Health NZ’s director of specialist mental health and addiction, said the rollout of phase two had so far gone well.
She assured the public that mental health support was still available.
“This change is about ensuring people requiring mental health support receive the right care at the right time, while maintaining the safety and wellbeing of patients and our staff.
“I’d like to assure the public there is a range of services to help people in mental distress or those who are concerned about the mental health of whānau.”
If a person was in serious mental distress or crisis, support could be sought from a local crisis team, she said.
If a situation was life-threatening, or someone was in immediate danger of harming themselves or others, police should be called.