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The email is from the head of the department, Andrew Kibblewhite.
It details survey results in which about 30% of people had either observed or experienced "verbal abuse, intimidation or exclusion".
The survey covered several areas, but the email was leaked by someone concerned about the findings around bullying.
DPMC has about 275 staff in Auckland, Wellington, and Christchurch, and describes itself as a having "a unique role as the trusted advisor, leader, and steward of our system of executive government".
It supports ministers with responsibilities relating to national security, intelligence, civil defence, child poverty reduction, and the regeneration of greater Christchurch.
National Party's state services spokesperson Nick Smith said the survey findings were "deeply concerning".
"That the Department of the Prime Minister and Cabinet, the premier state department, has got levels of bullying type behaviour being reported, is consistent with quite a lot of informal reports National is getting of a pretty dysfunctional Beehive.
"This shows these issues in this core department are quite serious, and the government's dysfunctionality extends deep into the senior public service."
In the 26 November email, DPMC head Andrew Kibblewhite said staff described unacceptable behaviour as including raised voices, disparaging comments, rude or belittling junior staff members, talking over others in meetings, favouritism, exclusion, abruptness, unreasonable workload expectations, standing over someone, scapegoating and sarcasm.
He encouraged staff to "call out behaviours with the person" or raise them with a manager.
"We take all reports of this nature seriously, and they will not be tolerated at DPMC", Mr Kibblewhite said in the email.
The survey was a follow up to an earlier one from July that delivered low results in three areas: remuneration, performance and behaviours.
The management team wanted more detailed information from staff and so conducted the second survey.
Speaking to RNZ, Mr Kibblewhite said only about 15 complained about being bullied but none of the behaviour was acceptable.
"It's when you go and look really closely and encourage people to dig around in their experiences that they haven't enjoyed so much you find things you don't like the sound of."
That was the case with this survey, he said.
"Favouritism, exclusion, abruptness, unreasonableness - none of those things are what you want in your workplace, so we're really keen to work with staff."
DPMC wanted to take the lead on this problem, Mr Kibblewhite said.
"We're not satisfied with a workplace where people are not fully happy, engaged and productive ... we want to do a whole lot better."