Australia is now in negotiations with three countries about taking some of the asylum seekers who are now in detention centres on Nauru and Manus Island.
Negotiations are under way with Malaysia, the Philippines and Indonesia, officials said, to allow the resettlement of asylum seekers.
Officials said the aim of “whittling away” the “legacy caseload” of asylum seekers who arrived under the Labor governments of Kevin Rudd and Julia Gillard was unchanged, but Prime Minister Malcolm Turnbull had brought “new energy and focus” to the quest.
“I want this settled,” Mr Turnbull instructed a senior official soon after taking the prime ministership.
A total of 1459 people were in detention in Australia’s facilities in Nauru and Manus Island last month, according to the Immigration Department.
The government, like Labor, says no one who seeks to enter Australia by boat will ever be permitted to resettle in Australia.
But, in cases where asylum seekers are found to be legitimate refugees, they cannot be sent back to their home countries, either.
The resettlement deals that Australia has made so far have proved to be failures, with no asylum seekers prepared to resettle in PNG and only five opting to move to Cambodia.
Officials said negotiations were afoot with Malaysia and the Philippines for resettlement of asylum seekers now in offshore detention.
With Indonesia, the question is whether Jakarta will agree to take back people who boarded boats to Australia, who will never be permitted to settle in Australia but who still have family or other connections in Indonesia.
Officials said there was a prospect of agreement with one or more “in months, not weeks”.
Foreign Affairs Minister Julie Bishop, while not confirming the names of the countries now engaged in negotiations with Australia, cautioned that “it’s early days for most of the discussions”.
“Some of them have domestic issues, like elections.”
The Philippines has presidential elections in May. Malaysia is in the grip of a corruption scandal that has embroiled Prime Minister Najib Razak.
Australia has had fruitless discussions with both countries in earlier years.
Malaysia had agreed to take asylum seekers from Australia under Labor’s so-called “Malaysia solution” as part of a swap, but the deal was struck down by the High Court.
And Australia approached the Philippines last year on the matter, but was rebuffed last October by President Benigno Aquino, who said at the time that his government was “challenged to meet the needs of its own people right now”.
Fresh negotiations were now under way, officials said.
Mr Turnbull on Friday ruled out accepting New Zealand’s offer to take 150 asylum seekers from Australia’s offshore detention centres.
In a joint appearance with his NZ counterpart, John Key, he said: “We are utterly committed to ensuring that we give no encouragement, no marketing opportunities to the people smugglers.”
While Cambodia and PNG are too poor and unattractive as resettlement options, Australia considers NZ to be too wealthy and attractive, a potential draw for a new wave of people smugglers carrying asylum seekers.
Australian officialdom believes that democratic, middle income countries such as Malaysia, the Philippines and Indonesia are the ideal resettlement option.
Labor’s immigration spokesman, Richard Marles, responding to revelations of the new negotiations, said: “Offshore processing remains a critical deterrent to people smuggling. However, the long-term viability of this policy rests on Australia securing a viable third country resettlement plan.
“We simply must find a durable resettlement solution. A failure to do so will result in tremendous harm being done to this group of men, women and children.”