Ulu said the safety of teams was a priority and the DHB was working to provide security support, including with Māori Wardens. Police have also been brought in when required.
"Our teams are doing the best they can to administer Covid-19 tests and distribute rapid antigen tests but, across the board, are experiencing an unacceptable level of abusive behaviour."
"This is not only distressing for our teams and members of the public who witness this sort of behaviour, it compromises our ability to keep collection points running and to stand up additional capacity."
Wellington has seen massive demand for RATs; queues of cars have been lined up at collection points, causing traffic chaos throughout the city.
To combat this, Sky Stadium has replaced the Hataitai netball courts as the main public collection point for RATs and will be open seven days a week to try and address the demand.
The Taranaki St testing centre will also distribute RATs, as will the Waikanae Rugby Club. The Canons Creek site in Porirua is closed today because of a large funeral nearby, but will be open as normal from 10am Saturday.
"People should only visit CTCs to collect tests if they have symptoms or live with someone who has Covid-19. Our teams will prioritise distribution along these lines, and each box contains five tests that can be used by household members.
"We understand that this is a scary and stressful situation for many people. However, our staff are doing the best they can and deserve respect and kindness while they do their work."
The Ministry of Health reported there are 1356 new cases of the virus in the Capital & Coast District Health Board area today; 17 people are in hospital.
There are 577 new community cases in Hutt Valley, and five people in hospital.
Across the country there are 22,527 new cases and 562 people in hospital.
The majority of new cases are being detected with RATs.
"The ministry wants to reassure people that we have enough RATs to help New Zealand through a widespread Omicron outbreak in the coming months.
"So, while we are anticipating continued high demand, our request is to, please, be patient and kind to each other and staff. They are working as hard as they can."
Over the past week, 8.8 million RATs have been distributed. Over the weekend, another 8 million RATs are expected to arrive in the country. Another 99 million are confirmed for delivery this month.