In announcing the deal yesterday, Prime Minister Malcolm Turnbull would not say whether he had discussed it with Trump during their telephone conversation on Thursday.
"We deal with one administration at a time and you don't discuss confidential matters with one administration with a future administration," Turnbull told Nine Network television.
Turnbull could not say whether the refugees would be resettled before the Trump administration takes over on Jan. 20. The numbers and timing would be decided by the United States.
Trump has called for a moratorium or tight restrictions on Muslim immigration. Most of the asylum seekers are Muslims from the Middle East, Africa and Asia.
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Turnbull said negotiations on the deal began with a conversation he had with President Barack Obama in January.
US Secretary of State John Kerry confirmed that the United States had "agreed to consider referrals" from the United Nations refugee agency on Australia's refugees.
Australia refuses to resettle any refugee who has arrived by boat since the date the tough policy was announced on July 19, 2013.
Any refugee who refuses to go to the US would be given a 20-year visa to stay on Nauru, a tiny impoverished atoll with a population of 10,000 people, Immigration Minister Peter Dutton said.
The Refugee Council of Australia, an advocacy group, welcomed the deal as a vital first step in ending the indefinite detention of asylum seekers on the islands. The London-based rights group Amnesty International accused Australia of taking "an extreme step in shirking responsibility."
Turnbull said at the time that the agreement to resettle Hondurans and Salvadorans was "not linked to any other resettlement discussions" involving Australia's refugees getting to the US.
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