New Zealand will spend $NZ3 million ($A2.7 million) to provide essential services for refugees and asylum seekers on Manus Island and Nauru while still putting pressure on Australia to accept an offer to resettle 150 people.

NZ Prime Minister Jacinda Ardern revealed the spend after a second conversation in two days with Prime Minister Malcolm Turnbull over Canberra's handling of the issue.

Meetings have also been held by officials from both sides and the Kiwis will begin work to expedite processing if and when the offer is taken up.

That is more progress than New Zealand has seen on the offer, first made by former prime minister John Key four years ago, in some time, Ms Ardern said.

But it's still expected to take around five months to process and resettle any refugees sent to New Zealand and there remains a need to care for those on the islands in the interim, she said.

"We intend to work with Papua New Guinea and other agencies like the International Red Cross to financially support them with any additional needs that they may need to be met while those refugees remain on the island," she announced in Manila late on Tuesday night (local time).

Australia is aware of that spend and Ms Ardern said she imagined they would be pleased rather than embarrassed to see New Zealand stepping in to assist with a resolution.

Meanwhile New Zealand's offer has strong support from within the parliament.

The Senate passed a motion on Tuesday afternoon calling on Mr Turnbull to accept New Zealand's offer.

Opposition Leader Bill Shorten has also urged Mr Turnbull to reconsider.

Ms Ardern has spoken to Mr Shorten about the offer, most recently in passing several weeks ago.

"I've seen public statements from him so I've seen his position on it but obviously we're working with the Australian government on the issue," she said.

The offer was first made to Labor prime minister Julia Gillard who rejected it.