US ties with Australia became strained this week after details about an acrimonious phone call between Trump and Australian Prime Minister Malcolm Turnbull emerged, and Trump said a deal between the two countries on refugee resettlement was "dumb".
About 1,000 people gathered in Sydney to protest against Trump's executive order on immigration and to call on Australia to close its offshore processing centres on the tiny Pacific island of Nauru and Manus island in Papua New Guinea.
Similar protests were held in Canberra, Newcastle and Hobart, and on Friday hundreds attended an anti-Trump rally in Melbourne.
Under the "dumb deal", the US would take up to 1,250 asylum seekers held on the islands. In return, Australia would take refugees from El Salvador, Guatemala and Honduras.
Trump has begrudgingly said he planned to stand by the deal, but a source said on Friday that US immigration officials had postponed interviews with asylum seekers on Nauru.
Trump's executive order last week suspended the US refugee programme for 120 days and stopped visits by travellers from seven Muslim-majority countries - Iran, Iraq, Libya, Somalia, Sudan, Syria, and Yemen - for 90 days.
A US judge on Friday put a nationwide block on Trump's executive order, although his administration could still have it reinstated on appeal.
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