The United Nations refugee agency says it struck a "clear understanding" over several meetings - which included direct discussions with Immigration Minister Peter Dutton - that some refugees from Manus Island and Nauru would be resettled in Australia.

In a statement jarringly at odds with the Turnbull government's public position that no refugees now in offshore detention would set foot in Australia, the UN High Commissioner for Refugees said the agency had agreed to help administer the deal between Australia and the United States on the understanding there would be exceptions for vulnerable people with family ties in Australia.

The angry statement accusing the government of failing to honour the understanding has led to an extraordinary public standoff between the UN agency and Mr Dutton, whose office on Monday dismissed the UN claim, saying the government had been clear about its position all along.

"Last November, UNHCR exceptionally agreed to help with the relocation of refugees to the United States following a bilateral agreement between Australia and the US," UN commissioner Filippo Grandi said in a statement released on Monday.