A federal judge on Saturday blocked part of President Donald Trump's temporary immigration ban, ordering authorities to stop deporting refugees and other travellers stuck at US airports.

The decision accompanied growing resistance to Trump's crackdown on Muslim immigration, with large protests spreading at major airports across the country.

“Victory!!!!!!” the American Civil Liberties Union (ACLU), whose lawyers sued the government, tweeted after US District Judge Ann Donnelly issued her decision.

“Our courts today worked as they should as bulwarks against government abuse or unconstitutional policies and orders.”

Trump's sweeping executive order, signed Friday, suspends the arrival of refugees for at least 120 days and bars visas for travellers from seven Muslim majority countries for the next three months.

The move, which was implemented immediately by US authorities, sparked large protests at major airports across the country.

At New York's John F. Kennedy International Airport, some of the 2,000 demonstrators there chanted “Let them in, let them in!”

Large protests took place at the main airports for Washington, Chicago, Minneapolis, Denver, Los Angeles, San Francisco and Dallas.

Donnelly's decision to issue a temporary stay ─ which stopped short of ruling on the constitutionality of Trump's order ─ came after dozens of people were detained at US airports following Trump's actions.

The exact number of those affected is unclear, but the judge ordered the government to provide lists of all those detained at US airports since the measure went into effect.

Sending those travellers back to their home countries following Trump's order exposes them to “substantial and irreparable injury,” wrote Donnelly, who was appointed by Trump's Democratic predecessor Barack Obama.

A second federal judge in Virginia also issued a temporary order restricting immigration authorities for seven days from deporting legal permanent residents detained at Dulles Airport just outside Washington, according to US media.

Trump originally asked for 'Muslim ban': Giuliani

Trump originally dubbed his executive order as a “Muslim ban,” according to the US president's aide Rudy Giuliani.

“When he first announced it he said, 'Muslim ban,'” the former New York mayor told Fox News late Saturday when asked whether the ban was connected to religion.

“Show me the right way to do it legally,” Giuliani ─ who Trump has tapped as his cyber security guru ─ said the US president told him.

The 72-year-old said he and a team of legal experts “focused on ─ instead of religion ─ danger!” when they drafted the immigration crackdown that has sparked a global outcry and mass protests.

Giuliani said those predominately Muslim countries were targeted because they are “the areas of the world that create danger for us.”

“Which is a factual basis, not a religious basis,” he said.

Explore: Muslim world's shock, outrage at Trump's visa ban

'We were prepared'

“We knew that was coming ─ we were prepared,” said Camille Mackler, a lawyer who heads legal initiatives at the New York Immigration Coalition, one of the groups that quickly mounted the demonstration there.

“But we didn't know when, and we couldn't believe it would be immediate, that there'd be people in an air plane the moment the order was taking effect.”

The List Project, which helps Iraqis whose personal safety is threatened because they have worked for the United States, expressed outraged over the move, warning it put American lives at risk too.

“I can't say this in blunt-enough terms: you can't s**** o*** the people that risked their lives and bled for this country without consequences,” wrote the project's founder and director Kirk Johnson.

The ACLU's legal challenge sought the release of two Iraqi men on grounds of unlawful detention. One of them ─ Hameed Khalid Darweesh, who has worked as interpreter and in other roles for the US in Iraq ─ was in fact released on Saturday after being detained the day before.

'We must fight'

Democratic Representative Jerrold Nadler, who went to JFK to press for the release of those detained under Trump's measure, said “We must fight this executive order in the streets, in the courts, anywhere, anytime. We must resist. We must fight.”

Trump's pronouncement on Muslim immigration makes good on one of his most controversial campaign promises to subject travellers from Islamic countries to “extreme vetting” ─ which he declared would make America safe from “radical terrorists.” The targeted countries are Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.

Donnelly's decision shows that “when President Trump enacts laws or executive orders that are unconstitutional, and illegal, the courts are there to defend everyone's rights,” ACLU executive director Anthony Romero said in leaving the emergency hearing.

The ban has triggered political backlash, including from Trump's fellow Republicans.

Orrin Hatch, the most senior Republican in the US Senate, spoke of America's “legal and moral obligations to help the innocent victims of these terrible conflicts.”

“I strongly urge the new administration to move quickly to tailor its policy on visa issuance as narrowly as possible, delivering on our security needs while reducing unnecessary burdens on the vast majority of visa-seekers that present a promise ─ not a threat ─ to our nation,” he said in a statement.

Connecticut Senator Chris Murphy, a Democrat, wrote: “To my colleagues: don't ever again lecture me on American moral leadership if you chose to be silent today.”

His tweet was accompanied by the now iconic photograph of Aylan Kurdi, a three-year-old Syrian boy whose body washed up on a beach in Turkey in 2015 after a failed attempt to flee Syria's brutal war to join relatives in Canada.

A long battle

The rapid mobilisation against the order suggests a protracted battle is shaping up between migrant advocates and Trump and his administration.

“This is the opening salvo of a long battle that will go on in the courts,” said Michael Kagan, a law professor at the University of Nevada Las Vegas who specialises in immigration issues.

He said the outcome of the legal battle is unclear because “we are in unchartered territory in modern America.”

The battle could end up in the US Supreme Court, which has not ruled on this type of immigration issue since the 1882 Chinese Exclusion Act.

A White House official said that holders of a green card ─ which allows permanent residence in the US and often takes years to obtain ─ who are abroad should first go to the US consulate to obtain a document allowing return to the US.

And green card holders in the US who want to travel abroad must obtain approval from a consulate official.

The State Department has said that people from the seven countries under the 90-day travel ban will be prohibited entry no matter their visa status.

Only those holding a dual citizenship with the US will be allowed to enter.