Now, the government is being accused of "disgraceful" conduct over an alleged "secret deal" with independent Tasmanian senator Jacqui Lambie, who said she can't speak about the situation due to national security concerns.
He said the medevac law was a "bad policy" that deserved to be voted out.
The Australian Senate has passed the government's so called medevac repeal bill, 37 votes to 35.
Lambie had indicated previously that her vote for the repeal would be conditional on the government meeting a condition which she would not specify.
Prior to the vote, Senator Lambie became emotional as she explained the reason for her decision.
A teary Lambie told the Senate "I'm not being coy or silly when I say I genuinely can't say what I proposed".
It's thought Australia may have agreed to send refugees from offshore processing to New Zealand after a similar arrangement with the United States ended. Repeal would deny people treatment, she said.
"The government is always looking at ways in which it can resettle those who are on Nauru".
"We will continue to use the arrangements that we have in place to be able to resettle people and that is the assurance that we have provided", he said.
"Senator Lambie is fully aware of the government's policies, and is pleased with those policies, and today she has supported those policies", Morrison said. I really don't understand this level of secrecy.
"We've worked to an outcome I believe we both want, which is an outcome that our borders are secure, the boats have stopped and sick people aren't dying waiting for treatment", she said.
Thirteen medical colleges and more than 5,000 doctors had warned against any attempt to wind back the medevac laws.
Morrison rejected those allegations, insisting Canberra has provided significant medical aid, while those unable to get necessary treatment can be sent to Australia if the minister for home affairs approves it.
He described the legislation as a law created to provide a "backdoor" to Australia, which was now closed.
"What I can say is that there has been no deal to change any policy on border protection or anything else".
Jacqui Lambie sided with the government, paving the way for the bill to be introduced.
The Medevac Bill, which passed despite the Morrison Government's best efforts to kill it dead at the time.
"Members of the cabinet of Australia are coming in to vote on a deal they haven't even seen", said Penny Wong, the Labor opposition's Senate leader.
"A deal between the Morrison government and Senator Lambie to drive a stake through the heart of medevac and they're keeping it secret from this parliament and from the Australian public".
The New Zealand immigration minister's office told AAP there was no formal request from Australia, but the offer remained on the table.
Jacqui Lambie after speaking in the Senate on Wednesday.
"Let me just make the most important point right up front - there is no secret deal", the Government's leader in the Senate, Mathias Cormann, told the Parliament.
When twice asked if the government's existing policy included resettling refugees to New Zealand once the U.S. resettlement deal was exhausted, Morrison said: "The government's policy is to ensure that we seek to resettle people who are on Nauru".
It cancels the medevac laws pushed through by the opposition in February that eased the transfer of sick refugees to Australia from offshore detention in Nauru and Papua New Guinea.
Since 2013, the nation has sent asylum seekers arriving by boat to detention centres on Nauru and Papua New Guinea (PNG).
Under medevac, two treating doctors could recommend a medical transfer to the Department of Home Affairs.
"But when I say I can't discuss it publicly due to national security concerns, I am being 100% honest to you".
The minister could also deny on health grounds - in this event it goes to the Independent Health Advice Panel for review. "I am more than satisfied that the conditions are now in place to allow medevac to be repealed".
With additional reporting from wires.