"The only undertaking we've given is to implement our policies – that's it,"Mr Morrison said.

"The government's policy is that we seek to resettle people who are on Nauru."

Asked several questions about any commitment to Senator Lambie,the Prime Minister said:"She has an assurance the government will implement its policies."

Asked if the New Zealand option could be on the table after settlements in the United States are exhausted,Mr Morrison said:"The government is always looking at ways in which it can resettle those who are on Nauru."

Home Affairs Minister Peter Dutton said 654 refugees had been settled in the US from Nauru and Manus Island,while another 251 had gained"provisional approval"to travel to the US and 21 of those approved refugees had come to Australia under the medevac rules.

Mr Dutton also rejected the argument from human rights groups that asylum seekers needed to come to Australia for treatment,arguing instead that asylum seekers were getting the help they needed in Papua New Guinea,Nauru or Taiwan.

Mr Dutton said 51 contracted health professionals were providing services to 258 people on Nauru and Manus Island.

The Coalition has 35 votes in the upper house and needs four of the six crossbenchers to gain the 39 votes required for a majority. It repealed medevac with support from Senator Lambie,independent Cory Bernardi and the two One Nation Senators,Pauline Hanson and Malcolm Roberts.

While the government avoided any show of jubilation after the vote,the outcome is a significant victory for Mr Morrison after last week'sdefeat on industrial relations law,adelay to religious discrimination law and weeks of questions overEnergy Minister Angus Taylor.

The government cleared the way for the final outcome with a series of procedural votes in the Senate that went ahead smoothly,with Senator Lambie never wavering in her support,guaranteeing the numbers against Labor,the Greens and Centre Alliance.

Labor Senate leader Penny Wong accused the government of striking a"deal that dare not speak its name"and attacked the attempts to force a vote in the Senate on Wednesday without full disclosure of any agreement.

The government leader in the upper house,Finance Minister Mathias Cormann,dismissed the attack by arguing Australians knew where the government stood on border protection.

"There is no secret deal. There is no secret,"he said.

When Labor attempted to stall the process by moving that the bill could only be considered after the government produced the documents showing its deal with Senator Lambie,the government secured the numbers to press ahead toward a final vote.

Senator Hanson argued for the restoration of the government regime by claiming asylum seekers were"swallowing stones"to claim the need for medical help in Australia so they could apply to stay.

"How many of those people have actually been sent back? None. They are using it as a back door to get into the country,"she said.

"We will be supporting this bill very,very strongly."

Speaking after the repeal,Senator Di Natale warned of the harm to asylum seekers.

"Medical care is a fundamental human right,and today the government,along with Senator Jacqui Lambie,voted to remove that fundamental human right to people who are suffering,"he said.

"It is cruel,it's brutal,and it is a sign that this is a government that will do whatever it takes to keep this secretive and brutal regime under a shroud of secrecy."