A federal judge has blocked the US government from deporting Muslim migrants and refugees who have been detained at US airports after President Donald Trump issued an order to severely restrict immigration from seven predominantly Muslim nations.

The New York judge ordered the temporary stay after human rights groups sued Mr Trump on behalf of two Iraqi men who were detained on Friday after landing at New York’s JFK airport. Judge Ann Donnelly said the two Iraqi men — and others in the same situation — had a “strong likelihood of success” of proving in court that their right to due process and equal protection had been violated.

Marielena Hincapie, executive director of the National Immigration Law Center, one of the groups that filed the legal challenge, said the stay was a “great first victory by immigrants and refugees against the Trump administration”. She said it was important because a number of other Muslims were being detained at airports across the country.

The Trump administration has sparked huge criticism from across the world over the executive order. Airlines began turning away passengers bound for the US after immigration officers at JFK detained the two Iraqi men, who possessed valid visas that they had been recently issued in exchange for having co-operated with the US in Iraq.

Mr Trump signed an order on Friday to create the first stage of the extreme vetting programme he promised during his presidential campaign. It barred refugees from entry for 120 days and indefinitely prohibited entry for Syrian refugees. It also prohibited citizens of seven Muslim nations — Syria, Iraq, Iran, Sudan, Libya, Somalia and Yemen — from entering the US for 90 days.

Speaking in the Oval Office on Saturday evening, Mr Trump defended the ban, which he said was “not a Muslim ban”.

“It’s working out very, very nicely,” he said. “We’re going to have a very, very strict ban and we’re going to have extreme vetting, which we should have had in this country.”

A Trump administration official said holders of green cards — permanent residents who do not hold citizenship — from the seven countries who were overseas would have to apply for a waiver to return to the US. The official said green card holders in the US would have to meet a consular official before leaving the country.

Protesters gathered at JFK airport during the day as the New York Taxi Workers Alliance was encouraging its drivers to join the protest. “Drivers stand in solidarity with refugees coming to America in search of peace and safety,” the alliance said.

“The president is putting professional drivers in more danger than they have been in any time since 9/11 when hate crimes against immigrants skyrocketed.”

Renée Paradis, a lawyer helping detainees at JFK, welcomed the stay but said that there was some confusion because “it requires those people be admitted, but not that they necessarily be released from detention”. She said there were at least a dozen people who were still being detained at the airport’s Terminal 4.

Anthony Romero, executive director of the American Civil Liberties Union, said the US legal system had worked as “bulwarks against government abuse or unconstitutional policies and orders” and that “Donald Trump suffered his first loss in court”.

The executive order has been lambasted by critics, ranging from Google and other companies to human rights groups and some foreign leaders. Justin Trudeau, the Canadian prime minister, said on Twitter that his country would welcome people fleeing persecution, terror and war, adding “diversity is our strength”.

Malala Yousafzai, the 19-year-old Pakistani shot by the Taliban as a schoolgirl who was awarded the Nobel Peace Prize, said she was “heartbroken” at the move.

“President Trump is closing the door on children, mothers and fathers fleeing violence and war,” she said. “I am heartbroken that America is turning its back on a proud history of welcoming refugees and immigrants — the people who helped build your country, ready to work hard in exchange for a fair chance at a new life.”

Critics have also castigated Mr Trump for saying that Christians from predominantly Muslim nations would receive priority when applying for refugee visas, a move that some argue would impose an unconstitutional religious test.

While Mr Trump signed a range of executive orders in his first week, the vetting programme has had the most immediate tangible impact. The visa ban will not only affect nationals from the seven majority-Muslim nations, but also people from those countries who are travelling on a different country’s passport, a state department official said. It should not affect dual nationality Americans, however.

During the presidential campaign, Mr Trump called for a complete ban on Muslims entering the US. His rhetoric sparked a harsh reaction from Democrats and many Republicans, who said such a move would be unconstitutional. At the time, the critics included Mike Pence, then governor of Indiana who now serves as the US vice-president.

Australians warned

The Department of Foreign Affairs and Trade (DFAT) updated its travel advice for the US with the warning that Australians who have travelled to any of the seven banned countries since March 1, 2011 will need the usual Electronic System for Travel Authorisation (ESTA) entry under the Visa Waiver Program.

DFAT said the ban would not apply to people travelling to the seven countries on official Australian Defence Force or government business.

It said the Secretary of Homeland Security may waive the travel restrictions on a case by case basis for a range of travellers to the countries including those working for charities, journalists and people visiting for legitimate business reasons.

In addition, Australians who are dual citizens of any of the seven affected countries are no longer eligible to apply for an ESTA.

“Any of these Australians who have previously been issued an ESTA are likely to have the ESTA revoked,” DFAT said.