National is calling for all people in contact with airline travel, no matter the extent, to be included in the testing regime.
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Leader Judith Collins and Covid-19 Response spokesperson Chris Bishop have spoken this afternoon.
Collins says she is concerned about how the outbreak happened.
Bishop says there "seems to be a question whether the person at the centre of this outbreak should have been tested or not. The suggestion last night was they should have been, then it has been clarifying that they were outside of the scope of the order today".
"Our strong recommendation is that that order ... be widened so that everyone, no matter if they have contact with international airlines or international travel, anyone working in and around the border, no matter which part of the company, they are tested.
"Secondly, our strong recommendation is that the auditing and monitoring of the companies - private and government - working at the border be significantly tightened up."
Bishop says using systems provided by the Ministry of Health should be mandatory for businesses involved with working at the border. He says the widening of testing should include all companies working at the border.
Collins says it is "simply not acceptable for New Zealanders to be forced into lockdowns which we have to have, when we find out that not all border staff are being tested, that the auditing of who is being tested seems to be somewhat voluntary.
"None of that is acceptable. These are opportunities for us to learn ... and do better."
Collins also welcomed the news that the first batch of vaccines had arrived in New Zealand, and said it was crucial those be rolled out as quickly as possible to frontline border staff.
She has today been calling for saliva testing to be compulsory at MIQs and for the people staying in the facilities.
Prime Minister Jacinda Ardern clarified at her post-Cabinet briefing that daily saliva testing was already in place in high-risk locations such as the Jet Park hotel, and may be rolled out further.