Attorneys in the United States have finished voicing their arguments in the biggest legal challenge to Donald Trump's travel ban so far.

They've been debating whether the ban on all travel from seven Muslim-majority nations is unfair discrimination.

Judge Richard Clifton points out it's common practice in international relations to treat people differently based on their nationality - and the US does it for Cuba and North Korea.

But Washington State solicitor general Noah Purcell said US immigration laws don't allow for this kind of discrimination.

"But not make this sort of 'across the board without exception' policy that applies to infants, children, grandmothers, to people who pose no plausible threat to this country."

The media's been dragged back into the controversy around the travel ban.

News articles around Mr Trump's campaign statements have been presented as proof that banning all Muslims was the true intention of the travel ban.

But a justice department lawyer arguing for the Trump administration said that proof isn't good enough.

He said it's extraordinary for a court to override the president's national security decision based on newspaper articles.

The lawyer doesn't deny the statements were made, but he said the court shouldn't take campaign promises into consideration.

The court's decision is likely to come later this week.