Up to 60,000 travellers to the United States had their visas revoked after President Donald Trump ordered a ban on visitors from seven Muslim-majority countries, according to the State Department.

The admission on Friday came hours after US media reports quoted a government lawyer as saying that about 100,000 travel visas had been cancelled following Trump's move.

A week ago, Trump issued an executive order halting arrivals for at least 90 days for the citizens of Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.

All refugee arrivals from around the world were also halted, in this case for 120 days.

"Fewer than 60,000 individuals' visas were provisionally revoked to comply with the Executive Order," Will Cocks, spokesman for the department's bureau of consular affairs, said on Friday.

"We recognise that those individuals are temporarily inconvenienced while we conduct our review under the Executive Order," he said.

During the 90-day ban period, the US administration will review visa procedures with a view to introducing what Trump has called "extreme vetting" to weed out suspected "extremists".

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US officials have denied the ban amounts to an anti-Muslim measure, despite the order saying "religious minorities" in the mainly Muslim countries will get priority treatment.

Trump said the move is needed to tighten US security against foreign "terror" threats, citing the September 11, 2001 attacks, despite the hijackers having no links to the named countries.

In the days after the move, dozens of visitors with valid visas and many with "green card" residency permits were detained on arrival at airports and many were sent back.

The White House has said 109 people were held for questioning upon arrival under Trump's executive order. US media have cited homeland security officials as saying many hundreds were denied boarding to the US as the ban was rolled out.

Meanwhile, four US states - Massachusetts, New York, Virginia and Washington - were in court on Friday mounting challenges to Trump's ban, with the challengers contending the move was unconstitutional.

The states' arguments focused on the ban's alleged targeting of people based on religion, which would violate the Establishment Clause of the US Constitution prohibiting the government from favouring one religion over another.

The White House has contended the moves were necessary for national security, and Department of Justice lawyers on Friday said religion had not been a factor in the selection of the seven countries.