Thousands of protesters rallied across Australia on Saturday condemning US President Donald Trump's order temporarily barring refugees and nationals from seven countries and demanding an end to Australia's offshore detention of asylum seekers.

US ties with Australia became strained on Thursday after details about an acrimonious phone call between Trump and Australian Prime Minister Malcolm Turnbull emerged and Trump said a deal between the two nations 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, while hundreds attended an anti-Trump rally in Melbourne.

Under the "dumb deal", the United States would take up to 1,250 asylum seekers held on Nauru and Manus. 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 told Reuters US immigration officials have postponed interviews with asylum seekers on Nauru.

In Sydney, protesters carried placards that said "Refugee torture, Australia's shame" and "No walls, no camps, no bans".

"Australia should not be trying to palm off people the government considers problems to the USA. We have the solution here," protester Beverley Fine, 62, told Reuters.

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 federal judge on Friday put a nationwide block on Trump's executive order, although his administration could still have the policy put back into effect on appeal.