Immigration New Zealand staff have been facing increasing abuse and threats from people in "desperate" situations.
A memo has set out measures to take against perpetrators to ensure staff wellbeing.
"Over the past few weeks Immigration New Zealand staff have received an increasing number of threatening emails and phone calls from individuals who are feeling desperate about their situation or the situation of their family," it said.
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"While as public servants we can empathise with their situation, it is not acceptable for our people to be subjected to abuse.
"INZ does not expect staff to tolerate this behaviour."
Employees have been told to report unacceptable behaviour, such as threatening to harm staff or others, or the use of profanities and offensive language.
Managers will then decide on actions, including speaking to the perpetrator and diverting or blocking correspondence.
In extreme cases, staff can contact police and the ministry's security team.
Immigration NZ said staff welfare was paramount and it offered counselling and specialist services.
"These sorts of challenging communications can, individually or cumulatively, take a toll on an individual's wellbeing and it is important that people look after themselves and take action before things become too serious."