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But Hipkins says that Clark made his own decision to resign, which was announced this morning, and Clark has rejected any claim that he was leaned on.
"He spoke to a number people, as you do, and he formed his own decision ... I didn't urge him to do anything," Hipkins told reporters today.
"I had a good, honest conversation with him, but he didn't do this because I told him he should."
Clark also told Hipkins that he was a potential blemish on Labour's chances of re-election in September, Hipkins said.
"That's certainly the view that Dr Clark himself formed."
Hipkins has taken over the Health portfolio, and he revealed that Clark had asked him if he would be interested in it.
"He indicated that was something that he would like ... David's a good friend of mine. He realised his presence in the role was becoming a distraction, or was already a distraction. It's a really rough call to make.
"It would be fair to say there have been a number of distractions."
Clark said he had become too much of a distraction and announced his resignation this morning, having offered it to Prime Minister Jacinda Ardern yesterday.
Ardern said they had a "very frank" discussion last week after video footage of Clark and Ashley Bloomfield went viral and sparked public outcry.
The video showed Clark saying that the director general of health was responsible for the bungles at the border, where people had left managed isolation or been granted compassionate leave without first being tested.
Bloomfield had already accepted responsibility and apologised, but he appeared dejected in the background as Clark repeated that it was Bloomfield's fault.
It caused an outrage online, with many calling for Clark's resignation and others fundraising to buy Bloomfield flowers, which were duly bought and delivered.
Ardern would not say if the video had been the straw that broke the camel's back, saying only that they talked about "some issues" that were getting in the way.
"We had a discussion around what we needed to do to keep Covid as a priority. It was his view that he needed to go.
"While Minister Clark made this decision, it is one that I agree with."
Clark said he had wanted to stay in the job until the Covid response was on a more stable footing.
He had previously offered to resign after he admitted to a beach excursion with his family while the country was in level 4 lockdown, but Ardern had rejected it at the time because of the need for continuity in the health response.
"What I wanted to see was that transition through to a stable footing because I believed that was the important thing. That indeed was what the Prime Minister pointed to when she didn't accept my resignation when I first put it," Clark said today.
"We've got to that position now. So the time is right."
Clark is no longer in Cabinet but will stand in the Dunedin North seat in September, and Ardern has not ruled out a ministerial position for him if Labour is re-elected - but not health.
National Party leader Todd Muller has been calling for Clark's head for weeks, and said the move was too little too late.
"The Prime Minister must take responsibility. She faced a huge test of her leadership and she failed. The question has to be asked; why did she repeatedly fail to fire him?"
Ardern has repeatedly backed Clark to keep health until the election.
Yesterday was the first time Clark had offered his resignation since the aftermath of the beach excursion, Ardern said.
"Ultimately it was his call and his judgment. He's put the team first. He's put New Zealand first."