National leader Todd Muller said Hamish Walker's resignation was "the only option".
The error of judgment in leaking Covid patients' details to media had "cost him his career", Muller said.
The events of the last few days had not reflected National Party values.
Muller wouldn't discuss the contents of a legal letter from a Queen's Counsel he had received on Monday, a day before Walker publicly confessed to leaking the patients' private details.
Walker quit politics today and will not stand as a National candidate for September's general election.
"Hamish has decided not to stand again... it's the right decision and now we look forward to identifying [a new] candidate," Muller told reporters in Ashburton.
"His judgment was fundamentally flawed."
Muller said it was not true to say that National had a track record of "dirty politics".
"One MP made a serious error and has paid the ultimate price," Muller said.
He said Walker had gone "behind my back" by leaking the patients' details.
Muller reiterated his earlier statement that he only became aware of the privacy breach at midday on Monday.
Former National Party president Michelle Boag, who gave the patients' details to Walker, had recused herself from any active role in the party, which showed how serious the issue was, Muller said.
The leaking of that personal information was "totally inappropriate".
"Of course I apologise."
Muller said the Government wasn't meeting Kiwis expectations around border management after revelations today that a hotel guest escaped and visited an Auckland supermarket last night, then testing positive for Covid today.
"They're everyday glitches," he said.
Muller made the comments after announcing plans for a $1.5 billion 60km expressway between Ashburton and Christchurch.
"This is part of our commitment to rebuild New Zealand," said Muller, who added the project would begin in 2023 if National was elected.
"Any questions about the road?" Muller asked the reporters, keen to steer questions away from the Walker leak.
Walker, National's first-term Clutha-Southland MP, confirmed earlier today that he was quitting politics and would not stand in the electorate for National in September's election.
"Today I am announcing that I will not be standing for re-election for the Southland electorate at the upcoming 2020 election," Walker said in a statement.
"I wish to thank the people of Clutha-Southland who I have loved meeting, assisting and representing over the past two and a half years. I sincerely apologise for my actions. I will be making no further comment."
Last night, Walker and former National Party president Michelle Boag confessed to being behind the massive privacy breach of Covid-19 patient information.
National leader Todd Muller said today he accepted Walker's decision to withdraw his candidacy for the seat of Southland and not stand at the upcoming election.
"Rachel Bird, the National Party's Southern Regional Chair, has received a letter from Hamish confirming he will withdraw as the National Party candidate for Southland.
"There was a clear breach of trust, which goes against the values National holds as a party. "The National Party Board will still meet today to discuss the selection of a new candidate."
The board was meeting to discuss Walker's fate but the MP fell on his sword.
Walker is not at home and a sign on his office says he is on "annual leave".
Walker was sent the information by Boag, who says she received it in her capacity as the acting chief executive of the Auckland Rescue Helicopter Trust Chair. She offered her resignation last night.
Auckland Rescue Helicopter Trust Chair Simon Tompkins says Boag's resignation was accepted.
"The breach which has been admitted by Ms Boag was of an email that was sent to her personal account," Tompkins said.
"As an administrative resource, Ms Boag has never had access to any clinical or patient data held by ARHT," he said.
"ARHT is an integral part of the health system and we are entrusted with information about our patients which is properly protected by protocols which only enable access to those who need this data to care for the patient. We have reviewed these protocols and are confident that none of this patient information has been subject to any privacy breach.
Nevertheless we take our responsibility for patient confidentiality very seriously and continuously seek to improve our protocols and procedures," Tompkins says.
"We want to reassure the New Zealand public and, most importantly, our patients and their families that patient care remains our top priority. Any information we hold on patients is private with access on a restricted basis and has not been breached."
Police Minister Stuart Nash believes an investigation will show other National Party MPs or members were also involved in Covid patient data leak.
"I simply can't believe that this is just Michelle Boag and Hamish Walker. There'll be others' fingerprints all over this," Police Minister Stuart Nash told Newstalk ZB this morning.
"Bill English and John Key would have handled this completely differently. This is a National Party problem at this point."
Muller earlier said there needed to be consequences for the leak and his advice to Walker was to "think deeply about what the honourable next step is".
Speaking to the Otago Daily Times in Oamaru, where he was attending a business breakfast at Whitestone Cheese cafe, Muller this morning said he was "hugely disappointed" in Walker's actions.
"I've made that point known to him and to the country."
Walker tried to stop Muller from publicly outing him as the leaker citing privacy concerns.
Walker admitted to Muller on Monday midday he was behind the private details of active Covid-19 cases being leaked to media, sparking a Government inquiry.
Muller told the Clutha-Southland MP he needed to own up publicly.
It's understood later that afternoon - after the Government announced the inquiry - Muller received a legal letter on Walker's behalf.
It asked the National Party leadership not to out Walker citing concerns about his privacy.
Muller then sought his own legal clarification.
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The National Party leader referred to this legal exchange with Walker in interviews this morning.
He told the AM Show: "I received a notification lunchtime Monday then asked Hamish to connect with my chief press secretary and chief of staff.
"And then, of course, we found out the inquiry was happening and it became very clear to me, very clear, that we needed to inform that inquiry of what we knew.
"I then shared that expectation with Hamish and then I received legal representation, which of course put me in a position of needing to check my own legal position before I made it very clear that that information needed to become public.
"That roughly that took 24 hours - it is what it is, that's how it happened. It was never going to be moved from the course that this information needed to be made public and it was."
A spokeswoman said given an inquiry had been announced and it was National's expectation that Walker "would be co-operating with that inquiry, both sides sought legal advice over what we could and could not say publicly, so that it didn't undermine the inquiry.
"And it took some to-ing and fro-ing before that came through."
The National Party leadership did not know former party president Michelle Boag was Walker's source until late Tuesday afternoon - hours before she outed herself in a press release.
Walker leaked the details of the patients to media on Thursday night as he believed by naming them, he would back up a claim the active cases were from "India, Pakistan and Korea" as he'd said in an earlier statement that was slammed as racist.
In his confession, Walker claimed he did it to "expose the Government's shortcomings so they could be rectified".
He said he'd sent the document to show the information wasn't password-protected or stored on a secure system which only authorised people could access.
After learning of Walker's role in the scandal, Muller immediately stripped the MP of his portfolios and wrote to the National Party board asking for him to be removed from the party.
It was also his "personal view" was Boag should step aside from having any involvement with the party.
Last night, Boag stood down from her role as acting chief executive of the Auckland Rescue Helicopter Trust - the role in which she'd received the patient's information.
She also today stood down from Auckland Central and deputy leader Nikki Kaye's campaign.
Boag said last night she'd made a "massive error of judgment on my part" and apologised for doing so.
"I very much regret my actions and did not anticipate that Hamish would choose to send it on to some media outlets but I am grateful that the media involved have chosen not to publish the 18 names that were contained within it."