A federal appeals court in San Francisco is hearing arguments for and against President Trump’s travel ban.
The executive order temporarily banned entry for all refugees and visitors from seven mainly Muslim countries.
Lawyers for the US Justice Department were first to make their case, urging the appeal judges to reinstate the order because Congress has authorised the president to control borders.
The orders were halted a week ago after two states challenged it.
They had said it was unconstitutional and harmed the interests of the states.
Whatever the 9th US Circuit Court of Appeals decides – and a ruling is unlikely to come on Tuesday – the case will probably end up in the Supreme Court.
A federal judge temporarily blocked Donald Trump’s order last week.
As a result, people from seven countries – Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen – with valid visas were able to travel to the US again.
Washington state, Minnesota and other states want the appeals court to permit the temporary restraining order to stand as their lawsuit works its way through the courts.
A 15-page brief issued by the Justice Department on Monday night argued the executive order was a “lawful exercise of the president’s authority” and not a ban on Muslims.