A government backbencher in Australia wants detainees on Manus Island and Nauru not accepted by the United States to be resettled in Australia.
The veteran MP Russell Broadbent made the call in a speech to parliament on Wednesday.
"Enough. El Shaddai. Shaddai, shaddai, enough," he told the house.
"I'm happy that the process with the Americans is working its way through very effectively at this time and there will be a resolution.
"Once that time comes it's time for this nation through its parliament to act and resolve this situation on Manus and Nauru. Shaddai."
Mr Broadbent's government drafted a bill last year to ban the detainees from returning to Australia, but the bill has yet to clear the Senate.
Further unease in Canberra over the regional processing of refugees was reported last week by the Australian.
The leader of the opposition Labor Party, Bill Shorten, urged the government to put "more energy" into moving asylum seekers from Manus Island.
"I think lot of Australians are concerned these people are still in these facilities," Mr Shorten said.
According to Fairfax a faction of Labor MPs confronted their immigration spokesperson, Shayne Neumann, last week with concerns for the welfare of people detained offshore.
The US vetting process for the detainees resumed this week following revelations from an American official about the resettlement deal struck between Australia and the Obama administration.
In Time magazine, the former deputy secretary of state Heather Higginbottom said the administration was uncomfortable with Australia's policy of offshore detention and lobbied for change.
She said President Barack Obama agreed to resettle up to 1200 refugees to relieve their suffering.
Australia's offshore detainees have been protesting this month with men on Manus Island marking their 17th day of peaceful demonstrations on Thursday.
With the Manus detention centre due to be closed by November, the men say power and water restrictions are an attempt to evict them into the PNG community.