With opponents of Donald Trump's travel ban arguing that it is motivated by religious discrimination, two key judges on the US Supreme Court indicated their support for the controversial ban on several Muslim-majority countries yesterday.

Chief Justice John Roberts and Justice Anthony Kennedy, the two most likely swing votes on the nine-judge court, both expressed disapproval over attempts to undermine Trump's authority on the issue.

Opponents want the Supreme Court to uphold lower court rulings striking down the ban, and as the justices began their first full consideration of the ban on Wednesday, Justice Elena Kagan – a Barack Obama appointee – posed an intriguing hypothetical for the court.

She asked what would happen if a presidential candidate was a 'vehement antisemite', elected after regularly making anti-Jewish statements, and upon taking office issued a proclamation barring immigrants from Israel.

Arguing on behalf of the Trump administration, Solicitor general Noel Francisco said this was a 'very tough hypothetical'.

Kagan replied: 'This is an out-of-the-box kind of president in my hypothetical.'

The Guardian pointed out that the exchange was emblematic of both the unprecedented nature of Trump's travel ban, which indefinitely bars more than 150 million people from gaining entry to the US, and the key issue before the court: was the president's action motivated by a genuine national security threat or by animus toward a particular religion?

The court is currently considering the third version of the travel ban, which bars or limits entry to citizens of five Muslim-majority countries – Iran, Libya, Somalia, Syria and Yemen – as well as North Korea.

The move also imposed travel restrictions on certain government officials from Venezuela and their families, but the restrictions against North Korea and Venezuela are not being challenged in court.

Human rights groups have warned that the travel ban is an attempt by Trump to deliver his campaign pledge to ban all Muslims from entering the US.

Lower courts have struck down three version of the travel ban, declaring it discriminatory on the basis of nationality and religion.

In December, the supreme court indicated that it may uphold Trump's policy by allowing it to go into effect while various legal challenges unfolded.

Among the challengers to the ban were Neal Katyal, the former acting solicitor general under Barack Obama, along with the state of Hawaii and other individuals who said they were directly affected by the ban.

But yesterday, indicating support for Trump, Kennedy suggested that the travel ban was not as indefinite as its opponents claimed and pointed out that its language included a review after 180 days.

'That indicates there will be a reassessment and the president has continuing discretion,' Kennedy said.

Roberts asked if the notion that Trump's actions were the result of bias meant that, for example, he could not carry out US air-strikes on Syria.

'Does that mean he can't because you would regard that as discriminating against a majority-Muslim country?' Roberts asked.

The conservative Justice Samuel Alito observed that the majority of the word's Muslims still had theoretical access to the US and said that the policy 'doesn't at all look like a Muslim ban'.

A ruling is not expected until June.