"She has the assurance that the government will implement its policies."

The refugees on Nauru are regarded as the most likely candidates for resettlement given that some of those on Manus Island in PNG have not gained refugee status and may not be accepted by New Zealand or other countries.

New Zealand Prime Minister Jacinda Ardern toldThe Sydney Morning HeraldandThe Age the offer remained on the table but emphasised it would cover people with approved refugee status.

"The Australian government knows that it's there,"she said.

While Senator Lambie was told of the risks of passing the medevac repeal without a detailed public commitment from Mr Morrison,the letter did not include any draft memorandum on the New Zealand agreement.

Asked if Senator Lambie had received the letter from Mr Morrison,the senator's spokeswoman would not comment.

The repeal hands more power to Home Affairs Minister Peter Dutton by restoring ministerial discretion on medical transfers and reversing medevac rules passed by Labor,the Greens and Centre Alliance in February to give doctors more say in transfers.

The Coalitionrepealed the medevac regime by 37 to 35 votes in the Senate with support from Senator Lambie,independent Cory Bernardi and the two One Nation senators,Pauline Hanson and Malcolm Roberts.

Senator Lambie told the Senate she was not being"coy or silly"but could not say what she proposed to the government to secure her agreement.

"I know that's frustrating to people. And I get that. I don't like holding things back like this. But when I say I can't discuss it publicly due to national security concerns,I am being 100 per cent honest to you,"she said.

Finance Minister Mathias Cormann said there was"no secret deal"with Senator Lambie,but Labor called for the release of any agreement on New Zealand or other options.

"What we saw today is that Minister Cormann said there was no deal[and] Jacqui Lambie said there was a deal,"said Labor home affairs spokeswoman Kristina Keneally.

"Clearly somebody is not being truthful with the Australian people. That's what happens when you do secret deals and then ask the Parliament to vote on them."

Senator Keneally said Labor would welcome an agreement to resettle refugees in New Zealand,given the option was first arranged in 2013 when Labor held government,but she questioned whether Mr Morrison would honour any undertakings to Senator Lambie.

GetUp human rights director Shen Narayanasamy said the medevac repeal was"devastating"because the law had saved lives by ensuring people were transferred to Australia for medical treatment.

"We all remember the crisis before medevac became law,12 people died offshore and people faced serious delays before they received medical treatment,"she said.

Mr Morrison told Parliament the restoration of the earlier regime would continue to ensure medical help was provided when needed and he attacked Labor for overseeing an increase in asylum seeker arrivals and detaining hundreds on Manus and Nauru.

Mr 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.

He said 57 people who had not been approved to go to the US had been transferred to Australia under the medevac laws.

The repeal means offshore asylum seekers will be required to apply under Section 198B of the Migration Act if they seek medical help in Australia.