ONLY a small minority of Australians trust US President Donald Trump to honour a deal to take refugees from Nauru and Manus Island.

And a substantial majority want the refugees settled on the Australian mainland should Mr Trump dud Prime Minister Malcolm Turnbull on the agreement.

The doubts about Mr Trump keeping his word are among the findings of an opinion survey commissioned by the Australia Institute think tank, and released today.

The responses highlight the Government’s dilemma. It is relying on the US to solve its problem of what to do with refugees Mr Turnbull has said will never come to Australia.

But they also identify a significant rejection of Liberal and Labor policy to keep even genuine asylum seekers out of the country.

“This polling shows that the two major parties are out of step with the majority of the Australian people who think that the refugees should be brought to Australia,” said deputy director of the Australia Institute, Ebony Bennett.

“After four years in power, we’re now faced with the imminent closure of the Manus Island detention centre and a government offering no solutions.”

Just 28 per cent of respondents agreed with the proposition Donald Trump would follow through on the deal reached by his predecessor

Barack Obama but which the new President has said he would carry out. Some 51 per cent disagreed with the proposition, according to the survey conducted by Research Now between April 28 and May 5.

A total of 72 per cent believe genuine refugees should be settled in Australia after processing.

The Government has repeatedly said that allowing asylum seekers on the mainland would encourage people smugglers to renew large-scale border incursions.

“The years that refugees have been languishing on Nauru and Manus Island represent a total policy failure by successive governments,” said Ms Bennett.

“After the Malaysia swap deal failure and the refusal to take up an offer from New Zealand to resettle refugees from offshore detention, the government has a painted itself into a corner. If the US deal does fall through, it would be a political and humanitarian disaster.”

The Government wants the Americans to speed up its intake of security-checked refugees.

The troubled asylum seeker processing centre on Manus Island will be closed by October 31 after the Papua-New Guinea government ordered an eviction late last year.

Detainees have the option of accepting third-party settlements including in PNG, or returning yo their homelands.