Queensland Police Minister Mark Ryan told the ABC: "I understand that 15 people have been now detained on behalf of the Australian Border Force and they will be assessed by the Australian Border Force and dealt with in accordance with Australian law." The search continues for at least two other people believed to remain on the run, including the boat's captain. A phone poll of 2261 people conducted by ReachTel for progressive lobby group GetUp! found that two-thirds of voters agreed Australia should "get refugee children off the island of Nauru" because children "shouldn’t be held in offshore detention" on the island. Almost half of those surveyed - or 47.4 per cent - strongly agreed with the proposition, and a further 20 per cent agreed. Police inspect a sunken fishing vessel, believed to be carrying Vietnamese asylum seekers, at Cape Kimberley at the mouth of the Daintree River in Queensland on Monday. Credit:AAP

About a third of voters either disagreed or strongly disagreed with the statement. Men were significantly more likely to disagree than women. More than 100 refugee children are believed to remain on the island, mostly living in the community. The most recent statistics from the Department of Home Affairs show 14 children were still detained at the regional processing centre as recently as June 30, alongside 182 men and 23 women. Loading The boat arrival comes at an inopportune time for the new Morrison government, given the Liberals' claim of having "claims to have "stopped the boats".

Mr Dutton blamed Labor for the boat arrival, telling Sky News on Monday: "I've warned the Labor party on talking time limits and how people if they stayed on Nauru and Manus would be there only for a limited amount of time and then end up in our country." He said the arrival demonstrated that the threat of people smugglers "hasn't gone away" and should be "a timely message". "I send a very clear message to people smugglers today: You won't succeed, not under this government," Mr Dutton said. "We have been very clear that we won't allow people that arrive illegally to settle in this country ... People will be deported from our country at the first available opportunity." Australia is legally obliged to process onshore the protection claims of people who arrive in the country.

He said it was believed that the vessel had set out for Australia from Vietnam. The strong support for removing minors from Nauru came as the ABC's 7.30 program revealed disturbing incidents of self-harm by refugee children on the island, contained in incident reports compiled by immigration workers. Loading One report from June this year said a 14-year-old had poured petrol over herself and obtained a lighter, while a 10-year-old had swallowed sharp metal objects. Children on Nauru were using Google to inform themselves about suicide, according to former health worker Fiona Owens, who spoke to the ABC.

Earlier, cabinet minister Steven Ciobo said detained foreigners should be rounded up and shipped off to immigration detention on Nauru. "Those people, if we can find them, they should be taken into custody, so to speak, and they should be sent to Nauru," Mr Ciobo told Sky News on Monday. "Or they should be sent somewhere offshore if we're able to do it under our international obligations." Amid last week's leadership challenge, the now-reinstated Mr Dutton said he would "love to get everybody off [Nauru and Manus Island] tomorrow". "If I could have brought them to Australia on a charter overnight I would have," he told Sky News after resigning his portfolio.

"But I would have seen people drown at sea, which would have been tragic obviously." The US continues to accept refugees from Nauru and Manus in line with the agreement struck by Malcolm Turnbull and Barack Obama to resettle up to 1250 people from the islands. A spokeswoman from the Department of Home Affairs said the Border Force has officers on site and is being supported by the Queensland Police Service in their search for the occupants of the fishing vessel. "We can confirm that a number of potential unlawful non-citizens have been located. The ABF and Department of Home Affairs will undertake the necessary border processes to establish circumstances around the arrival," she said. "As investigations into this matter are ongoing it would be inappropriate to comment further."