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One instance has been reported to police and the Ministry of Business Employment and Innovation staff have moved to responding to emails from a central address, rather than individual ones.
MBIE has received more than 18,000 emails about essential services during the Covid-19 pandemic.
Deputy chief executive Paul Stocks said MBIE was working hard to define what businesses were essential and which ones could continue to operate during alert level 4.
"We understand that this has been a very hard time for businesses, and acknowledge that for many, closing their business has had a huge impact on them, their employees and their families."
Stocks said a small number of emails have resulted in businesses expressing their frustration in a "non-constructive" way.
"This hasn't resulted in direct threats to any of our staff, but has resulted in a few instances of unwanted attention online or doxing."
"MBIE staff have worked above and beyond to help support businesses in this trying time. We continue to provide support to our staff so they feel they are able to do their jobs safely and to the best of their abilities."
He acknowledged businesses were under a lot of pressure but said that was true of staff fielding their queries as well.
"There's a lot of pressure on and they're doing a great job under really difficult circumstances, remember that the person you're talking to at the other end of the line is a human being and they should be treated with respect.
"If there's mutual respect businesses are better able to get quick solutions for the problems they're raising."
Stocks said MBIE was now using a system purposely designed for providing contact centre services, which meant responses were sent from a generic email address.
The move from individual emails to the new service meant there was a delay of a couple of days in responding to businesses with answers, Stocks said.
"While this transfer was happening, we continued to work behind the scenes so we could answer as many queries as we could as soon as the generic email was up and running. We are catching up as fast as possible."