Rotorua MP Todd McClay said he had received no threats he would describe as "significant".
"But there have been a few occasions when behaviour toward my staff has not been appropriate," he said.
"People can get very frustrated when engaging with their MP, but I draw the line when it flows over to my staff."
Waiariki MP and Maori Party co-leader Te Ururoa Flavell said in his nine years as an MP he had not received anything he would consider a threat.
"However, people have presented at my electorate office in the past with some concerning behaviour.
"I am mindful that people's individual circumstances can be stressful and that it is often hard to know where to direct anger and frustration.
"My staff know that their safety is the priority for me and should they feel threatened, they know what steps to take," Mr Flavell said.
New Zealand First list MP based in Rotorua Fletcher Tabuteau said he had received one threat that was "serious enough that parliamentary security insisted they intervene".
"I never felt personally threatened but the person involved had a track record," Mr Tabuteau said.
"They can worry you when they arise.
"But you cannot think about it otherwise.
"It was a threat from someone who had threatened MPs before. I worried for my staff in Wellington during that one," he said.
The authors of the paper said threats to MPs should be more closely monitored because politicians were often targeted by severely ill people who could pose a threat to the wider public.
The research paper, which was published in the Australian and New Zealand Journal of Psychiatry, said politicians felt they and their families were more exposed as a result of the internet.
They reported that cyberstalking and online harassment were common. Additional reporting NZME.
