The Australian immigration minister, Peter Dutton, says refugees from the Manus Island detention centre not taken by the US will be settled in Papua New Guinea, while non-refugees will be sent back to their home country, telling refugee advocates they can “bleat all they want” on the issue.

The comments were made after Malcolm Turnbull dodged questions about exactly where the government planned to send the men if the US did not accept them all under a deal struck by the Obama administration. The Australian prime minister said during a visit to Papua New Guinea that Australia had made “significant progress” towards resettling the nearly 900 men being held at the Manus Island detention centre, which is expected to close on 31 October.

“We are working to solutions, endurable solutions, of people who have been detained here and Nauru,” Turnbull told reporters after meeting with Papua New Guinea’s prime minister, Peter O’Neill. “Working with third countries most notably, of course, the United States, to that regard. We’ll take this process one step at a time.”

On Sunday, Dutton said people presently detained on Manus Island would not by coming to Australia when the Papua New Guinea centre closes, no matter how hard refugee advocates push.

“They are not coming to Australia,” Dutton told Sky News on Sunday. “The advocates can bleat all they want, they can protest all they want. We have been very clear those people are not going to settle in our country because that would restart the people trade.”

He said the threat from people smugglers and boat arrivals would “never go away” and he did not want to see people drowning at sea trying to get to Australia. Because of that, he said there would be an enduring need to keep the Nauru detention centre open.

Dutton said the government was working with the PNG government, the US Homeland Security and other state departments who are looking at each individual case in their decision who would be settled in the US.

“We think there is scope for a large number of people but we don’t have an exact number as yet,” he said.

He said that, under the agreement with the Rudd Labor government, PNG had the responsibility to settle refugees not taken by the US. He said 36 people had already settled in the PNG community. He said people found to be refugees on Nauru can be resettled in Cambodia, and some people had done that, or they could settle on Nauru under a 20-year visa agreement.

“The art here is to make sure we don’t do anything to restart boats [arrivals],” Dutton said.

The shadow immigration minister, Shayne Neumann, said while Labor supported 1,250 refugees from Manus and Nauru being resettled in the US, potentially hundreds would miss out.

He said the Turnbull government needed to clarify what the government’s role would be in Manus once the offshore processing centre closed in October and what support and assistance would be offered to refugees who were forced to remain in PNG.

“The Turnbull government has put all their eggs in one basket with the US agreement and failed to secure other third country resettlement arrangements,” Neumann said. “Immigration officials confirmed last month that the Turnbull government is not negotiating other resettlement options.”

In April 2016, O’Neill said he would close the Manus centre after the nation’s supreme court ruled that detaining asylum seekers and refugees there was a violation of their constitutional right to personal liberty. The decision sent Australian officials scrambling to find a place to resettle the detainees.

In November 2016 the Obama administration said the US would accept up to 1,250 refugees living on Nauru and Manus. But the US president, Donald Trump, was infuriated by the deal, dubbing it “dumb” and throwing the entire plan into doubt. Trump eventually agreed to honour the deal but has said the refugees will be subjected to “extreme vetting” before they are accepted. There are few details on what that would entail.

The refugees have the option of resettling in Papua New Guinea but few have agreed to do so. The vast majority have expressed concerns about a lack of job opportunities in the impoverished country, as well as safety fears.

“We cannot force people in a resettlement exercise,” O’Neill said. “But if a third country is willing to accept their resettlement, we are quite happy to participate.”

Asked whether those on Manus who are not accepted by the US could be resettled instead on Nauru, Turnbull said only, “We’ll take this process one step at a time.”

Turnbull’s visit to Papua New Guinea comes just days after the president of Nauru travelled to Sydney to discuss the fate of hundreds of refugees in limbo at his country’s detention camp.

The president of Nauru, Baron Waqa, insisted on Thursday that Australia’s asylum seeker program was “working well” despite the uncertain future of those stuck on the island.

With Australian Associated Press