"We agreed it was time for some new leadership,"the Prime Minister said.
"But going forward,I expect I will call on him from time to time as other ministers will,in meeting challenges and difficult issues in the future."
Dr Parkinson,who stepped into the role under former prime minister Malcolm Turnbull in 2016,said he wanted to give Mr Morrison the chance to work with a new department head.
"He is at the beginning of the term. He has a full agenda. And I came to the view it was better all around that he had someone who could go the full term with him,"he toldThe Australiannewspaper.
"I would not want anyone to think there was anything about my relationship with the Prime Minister that was leading me to leave.
"It is up to others to judge,but I think what he would tell you is that he and I have a very good personal and professional relationship."
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Mr Morrison is preparing to make significant changes to the public sector,based on the draft recommendations of areview led by former Telstra boss David Thodey.
Dr Parkinson,who initiated the probe,says further reforms are needed,including technological changes and ending the idea that people work in silos.
"What I want is a public service that is knowledge-based,curious,looking all the time for how existing policies are working,at what future policies should be,engaged in collaborating with people inside the public service as well as outside,"he said.
Less than a week after the federal election in May,Mr Morrison told public servants to brace for a hectic three years and"very clear"performance targets.
On Thursday,he made it clear the public service should not drive policy.
"It is the job of the public service to advise you of the challenges that may present to a government in implementing its agenda,"he said.
"But the government sets policy.
"The public service will rightly,and always do,in my experience,be very full and frank in what they say to me as Prime Minister. But once the government policy is set,it's their job to implement it."
The Prime Minister did not rule out further moves at the top of the public service,saying he reserved his right to make changes where he saw necessary.
AAP