A longstanding offer from New Zealand to resettle up to 150 asylum seekers in Australia’s offshore detention centres has been accepted in principle.

If a deal is struck, it means asylum seekers, some who have been held indefinitely in limbo in such centres on Manus Island and Nauru, could soon be settled in New Zealand.

An agreement was struck “in principle” in the Senate this week but will see further negotiations, including Australia seeking a guarantee there would be no “backdoor” for the people transferred to come to Australia.

Australia’s Home Affairs secretary Mike Pezzullo told the Senate the two countries had been in extensive negotiations at ministerial level and the matter was currently before the New Zealand Cabinet for its final approval.

Refugee activists welcomed confirmation that a final round of negotiations between both governments would take place over coming weeks.

Amnesty International Australia refugee adviser Graham Thom said he hoped the deal to settle 150 refugees a year from would be announced soon.

“New Zealand’s generous offer has been on the table since 2013 – it’s encouraging to hear it’s so close to being finalised, but now the government has to act and get it done,” Dr Thom said.

He said it was past time the asylum seekers were given a chance to rebuild their lives in safety and freedom.

Home Affairs secretary Mike Pezzullo confirmed in a Senate estimates committee hearing on Monday that the matter would go back for a final round of negotiations over the coming weeks.

Mr Pezzullo agreed with Labor senator Raff Ciccone’s characterisation that there had been an “in principle” deal, but he cautioned the Australian government still had concerns.

He said Australia wanted a guarantee there would be no “backdoor” for the people transferred to come to Australia.

“So, we are still working on those issues with the New Zealanders,” Mr Pezzullo said.

“There is an issue given the trans-Tasman travel arrangements whereby, after a period of time, a special purpose 444 visa would become available to a person.”

Home Affairs deputy secretary Marc Ablong said the “final set of those negotiations is expected in the next few weeks on the New Zealand side as to where their position lies”.

It’ll have to go through the New Zealand cabinet process before they come to us with their final position.”

The New Zealand Ministry of Foreign Affairs and Trade said its offer to resettle refugees still stands and the “final agreement on terms and timing is still to be decided by cabinet”.

“Any refugees considered by New Zealand for resettlement would undergo our comprehensive assessment and screening processes, which applies to all refugees

The NZ offer has been repeatedly rejected by the Australian government since a failed attempt to legislate a lifetime visa ban to stop them returning to Australia at a later date.

Home Affairs Minister Karen Andrews confirmed last year she was working with her New Zealand counterparts to resettle asylum seekers, with a separate refugee transfer arrangement with the United States coming to a close.

There are about 111 asylum seekers on Nauru, 104 in Papua New Guinea and hundreds on the mainland both in the community and in detention centres.

Refugee advocate and former Socceroo Craig Foster also welcomed the fact that the potential deal could be done within weeks, saying “all people deserve safety and a bright future”.