Eyre said public health's focus remained on contact tracing to identify anyone who may have come into contact with passengers or crew from the Ruby Princess cruise ship, which docked in Napier on March 15.
"Anyone who believes they were in close contact with Ruby Princess passenger or crew and has developed Covid-19 symptoms in the past fortnight is strongly advised to contact their GP so they could be assessed for referral to a Community-Based Assessment Centre (CBAC) for testing," Eyre said.
She reminded people that they needed an appointment at a CBAC before they could be assessed.
"But we do rely on clinical judgement at all times," she said.
Anyone with respiratory symptoms consistent with Covid-19 should now be tested regardless of whether they had been overseas or in close contact with a confirmed case.
About 1843 tests per day were conducted in the past week, with daily capacity at about 3700 tests.
More testing capacity is being added, she said.
A number of clusters, or outbreaks from connected cases, had sprung up, McElnay said.
On Monday a photo of a half-cauliflower for sale for $7 at Pak'nSave Napier was widely shared on social media, with commenters mostly fuming at the price.
At the Prime Minister's coronavirus update on Wednesday, Jacinda Ardern said about 990 emails had so far been sent to the government's newly set up email system to alert authorities about alleged price-gouging.
Ardern said the most common complaint was the high price of cauliflower, but hand sanitiser, bread, meat and garlic also featured.
"The process for dealing with complaints is being worked through and we will involve traders so they have a chance to respond," she said.