The opposition Labor party responded to Morrison's announcement calling it "scare tactics" and accused the prime minister of manufacturing a fear of migrants to win votes.
Prime Minister Morrison warns that the new law will weaken the country's strict border policies.
On Tuesday and Wednesday parliament rebuffed government warnings and adopted legislation opening the door for some of the 1,000 refugees detained in existing offshore centres on Nauru and Papua New Guinea's Manus Island to travel to Australia for medical treatment if the transfers are requested by two or more doctors.
The changes included a provision that only the 1,000 asylum seekers now held on Nauru and Papua New Guinea and not any future arrivals would be considered for medical evacuation under the new regime.
It was not clear if the government plans to treat asylum seekers on Christmas Island, thereby denying them access to the mainland, a lawyer for a refugee advocacy group said.
"It should come as no surprise to people that people smugglers have heard what is going on", Mr Dutton said.
Mr Morrison declared national security measures would be strengthened under the government's Operation Sovereign Borders after the medivac bill was passed.
Labor made a strategic move to avoid turning the bill into a test of confidence in the government, withdrawing part of the medical transfer scheme that required funding to pay for medical experts to review transfers.
"The government tells us that this bill is a constitutional crisis".
The 'cool' parenting tip Anne Hathaway got from Prince William and Kate
She also took the stage during the conference to speak about the importance of mental health education and training. Kate has spoken previously of her struggles with becoming a mum .
Most refugees who arrived by boat have gone into the community in the past.
Section 53 is "non-justiciable" and therefore a court will not decide if a law is valid, meaning the government can not challenge the medical transfer bill in the High Court.
He said the Christmas Island facility was on "hot contingency" alert for any new arrivals.
He pointed out the medivac bill only applied to asylum seekers and refugees now stranded on Manus Island and Nauru.
The Department of Home Affairs told the government last week it was aware of 300 cases of people on Manus Island and Nauru likely to be recommended for medical transfer under the new law.
Yes, the government is wielding its reluctance to provide Australian medical care, and its use of harsh facilities like Christmas Island, as an apparent weapon against asylum seekers.
Also in the Swiss city on Wednesday night, Abdul Aziz Muhamat, a Sudanese refugee activist who has spent five years on Manus Island, won the Martin Ennals Award 2019, one of the most prestigious global human rights prizes, organisers said.
Kerryn Phelps, the independent MP who championed the bill and who previously served as President of the Australian Medical Association (AMA), described the vote as "such an important day for sick people needing medical care they are unable to receive".