Elon Musk's Tesla Inc and SpaceX on Monday joined a legal brief filed by businesses opposed to US President Donald Trump's order restricting immigration from seven Muslim-majority countries, according to a court filing.

Musk agreed to become part of Trump's business advisory council in December, and has advocated discussing issues directly with the president. Uber chief executive Travis Kalanick quit the council last week amid mounting pressure over Trump's immigration policies.

Nearly 100 companies, including high-tech, joined a legal brief opposing President Trump's temporary travel ban, arguing that it would give companies incentives to move jobs outside the United States.

The companies - including Apple, Google and Microsoft - banded together late on Sunday to file a "friend-of-the-court" brief with the 9th US Circuit Court of Appeals in San Francisco arguing that the ban "inflicts significant harm on American business".

The companies, backing a lawsuit brought against the ban by Washington state, argued that Trump's order created uncertainty for companies depending on talent from overseas and global business travel to innovate and create jobs in the United States.

The fierce battle over Trump's travel and refugee ban edged up the judicial escalator Monday, headed for a possible final face-off at the Supreme Court.

Travelers, temporarily unbound, tearfully reunited with loved ones at US airports.

The Justice Department filed a new defense of Trump's ban on travelers from seven predominantly Muslim nations as a federal appeals court weighs whether to restore the administration's executive order.

The lawyers said the travel ban was a "lawful exercise" of the president's authority to protect national security and said a judge's order that put the policy on hold should be overruled.

The filing with the San Francisco-based 9th US Circuit Court of Appeals was the latest salvo in a high-stakes legal fight surrounding Trump's order, which was halted Friday by a federal judge in Washington state.

The judges are to hear arguments Tuesday.

The appeals court earlier refused to immediately reinstate the ban, and lawyers for Washington and Minnesota - two states challenging it - argued anew on Monday that any resumption would "unleash chaos again", separating families and stranding university students.

Trump's Jan 27 executive order temporarily barred entry into the United States of people from seven Muslim-majority nations as well as suspending the US refugee program, sparking protests and chaos at US and overseas airports.

Pending the next ruling in the case, the travel ban remained suspended, and people with valid visas who had been blocked from travel were being allowed to board planes. Refugee resettlement also resumed.

Facebook, Twitter, Intel, eBay, Netflix and Uber Technologies joined the brief, as well as non-tech companies such as Levi Strauss & Co and Chobani.