According to the order, Syrian refugees are banned from entry until further notice.
Nationals of six further countries, including Iran and Iraq, will be banned from entering the US for 90 days.
The entire US refugee admissions program is suspended for 120 days, and a lower cap on numbers introduced.
On January 28, several Iraqi passengers and a Yemeni national were prevented from boarding a flight at Cairo airport bound for New York, despite holding valid visas for the US.
The American Civil Liberties Union says it has filed a suit challenging the executive order. The Council on American Islamic Relations (CAIR) also says it will file a lawsuit.
The new restrictions will have a major impact on technology companies that hire skilled staff from all over the world on special H1-B visas.
There have been reports that “green card” holders, who are legal permanent residents of the US, being prevented from getting on flights. However, green cards are not specifically mentioned in the executive order, and so the status of green card holders remains unclear.
CAIR advised non-US citizens, including permanent residents, from the seven countries to plan to delay all international travel for at least 90 days.
President Trump said the measures detailed in his executive order would “keep radical Islamic terrorists out of the US”.
However, rights groups say there is no link between Syrian refugees in the US and terrorism.
Donald Trump signed the order on January 27, which was International Holocaust Remembrance Day.
His statement to mark that occasion, on the 72nd anniversary of the liberation of Auschwitz, made no mention of Jews or anti-Semitism.
The sudden and severe immigration restrictions imposed on passport holders from seven Muslim countries could seriously demonstrate the law of unintended consequences. The president wants to restrict some Muslims but the effect could be to damage America’s most important and profitable sector: technology.
Google has recalled around 100 of its affected staff from overseas. Microsoft has warned its shareholders that curbs on immigration could have a material impact on its business.
The technology sector relies heavily on highly skilled and well-paid workers from overseas on H1-B visas. If there’s a risk, however small, that that brainpower could be restricted in some way or scare off others who may feel unwelcome, the big tech companies may have to rethink where they place their key staff in future.
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