WASHINGTON - US President Donald Trump has called for a "much tougher version" of his travel ban and an "expedited" hearing for the measure before the Supreme Court.

In a series of early morning tweets, the president also said the United States was already "extreme vetting" travelers coming into the country for safety reasons.

"The Justice Department should have stayed with the original Travel Ban, not the watered down, politically correct version they submitted to the Supreme Court," Trump said.

"The Justice Department should ask for an expedited hearing of the watered down Travel Ban before the Supreme Court and seek much tougher version!"

In a rare move on Friday, the Supreme Court expedited consideration of the case, ordering the American Civil Liberties Union - which represents the plaintiffs - to respond by June 12 to the Trump administration's petition for court consideration.

Once it receives the response the high court could quickly rule on whether to take up the case.

The court's order came just one day after the Trump administration asked the court to reinstate its temporary ban on travelers from six Muslim majority nations, requesting it stay two nationwide blocks of the measure that had been issued by appellate courts.

Trump issued his initial travel ban by executive order in January, but that measure - which banned entry to nationals from seven countries for 90 days and suspended the nation's refugee program for 120 days - was quickly halted by the courts.

The administration said the travel ban was needed so it could evaluate existing screening protocols and set new ones.

The order however was widely criticized, including by human rights activists and US states led by Democrats.

Meanwhile, the US tourism industry faces the possibility of another "lost decade" of foreign visitors due to Trump's travel ban, a leading hotel executive said on Monday.

Jonathan Tisch, chief executive of Loews Hotel & Co, warned that policies viewed as hostile to foreign visitors could damage the US industry, much as a visa crackdown and other policies after Sept 11, 2001 attacks led to the loss of billions of dollars in revenues from overseas travelers.

"When it comes to a business as competitive as travel, we need to remember that words matter. Perceptions matter," Tisch said at a hospitality conference hosted by New York University.

"In other words, it's important to balance security measures designed to keep out people who mean us harm ... with words and actions assuring legitimate travelers that we welcome them and their business."

Afp - Ap