The second new death was a man in his 70s from Christchurch's Rosewood rest home, where eight others have died.
The new deaths take New Zealand's total toll to 16.
Medical Officer of Health Dr Nick Jones said Hawke's Bay District Health Board and Health Hawke's Bay (PHO) would be working with local healthcare providers to increase testing of people with symptoms in Wairoa and Central Hawke's Bay's rural areas over the coming days.
"These areas have had lower testing rates and it was important to ensure there were no cases of Covid-19 that have gone undetected.
"We are working through how we will be doing this today and will be able to announce the details tomorrow.
"Part of the plan is likely to include mobile testing in these areas and setting up satellite testing hubs.
"We are working out how we do this so it's easy for people in remote areas to access. The aim of any testing will be to test people with symptoms rather than random testing of well people.
"It's very important, that as we come out of the level 4 lockdown period, we are confident there are no Covid-19 cases that we don't know about," he said.
Jones reminded essential service workers to be tested if they had any symptoms given they had spent more time out of their "bubble" during the level 4 lockdown period, than others.
"Any essential worker feeling unwell should stay home and call their GP or Healthline for free on 0800 358 5453 to be assessed for testing.
"They should also be reassured of income support if they needed to stay home because of Covid as essential worker leave support is available through Work and Income New Zealand for these situations," he said.
Symptoms of Covid-19 include cold or flu-like illness with one or more of the following: a fever, cough, sore throat, shortness of breath, a runny nose or loss of smell.
• Covid19.govt.nz: The Government's official Covid-19 advisory website
