Google has recalled travelling staff members to the US after an executive order from President Donald Trump restricting entry for nationals of seven Muslim-majority countries.
Syrian refugees are banned from entry until further notice.
Visas for nationals of six countries, including Iran and Iraq, will not be issued for the next three months.
Google has told the BBC it is concerned about the order and any measures which could block great talent from the US.
The BBC's business correspondent Joe Lynam says President Trump's order means that thousands of citizens from Iran, Iraq, Syria, Yemen, Sudan, Somalia and Libya may not be allowed to board flights bound for the US - even if they hold a so-called "green card" (permanent residents' permit).
Mr Trump said the measure would "keep radical Islamic terrorists out of the US".
But rights groups say there is no link between Syrian refugees in the US and terrorism.
There are already reports of travellers from the countries targeted being turned away as they try to board flights to the US.
The American-Arab Anti-Discrimination Committee
said this appeared to include "green card holders and other visa holders".
It advised nationals from the affected countries but living in the US not to travel abroad.
Some Republicans have welcomed Mr Trump's announcement, including the Speaker of the House of Representatives, Paul Ryan, who said it was "time to re-evaluate and strengthen the visa vetting process".
The new policy is also affecting visits from relatives.
An Iraqi journalist living in the US, Mohammed al-Rawi,
posted on Facebook, saying his father had been turned away from a Los Angeles-bound flight in Qatar.
Jamal Abdi from the National Iranian American Council told the investigative journalism organisation
Pro Publica: "We are inundated with calls and questions of how this is going to affect people."
The Council on American Islamic Relations
says it will file a lawsuit against the executive order.
Silicon Valley, where many employed in the technology industry are of non-US origin, is also worried.
Facebook founder Mark Zuckerberg
posted a lengthy note, saying he was "concerned" about the president's executive orders, and noting that he, like many Americans, is the descendant of immigrants.
Four-month suspensionUnder Mr Trump's wide-ranging executive order, all refugee admissions have been suspended for four months.
The text of the order was released several hours after it was signed. Other measures include:
- A ban on refugees from Syria until "significant changes" are made
- A 90-day suspension on anyone arriving from Iraq, Syria, Iran, Libya, Somalia, Sudan, and Yemen, except certain visa categories such as diplomats
- Priority for future refugee applications from those persecuted for their religion - but only if the person is part of a minority religion in their home country
- A cap of 50,000 refugees in 2017 - less than half of the upper limit under Mr Trump's predecessor, Barack Obama
The order also said all immigration programmes should include questions to "evaluate the applicant's likelihood of becoming a positively contributing member of society."
In a TV interview broadcast earlier on Friday, the president said Christians would be given priority among Syrians who apply for refugee status in the future.
Other measures include a broad review of the information required from all countries to approve a visa; a review of visa schemes between nations to ensure they are "truly reciprocal" for US citizens; and the immediate suspension of the Visa Interview Waiver Programme.
But the document says exceptions to most restrictions could be made on a case-by-case basis.
During the election campaign, Mr Trump suggested a "total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on".
The executive order has been met with criticism from rights organisations, Democrats and notable figures.
Democratic Senator Kamala Harris noted that the order had been signed on Holocaust Memorial Day. "Make no mistake - this is a Muslim ban," she wrote.
"During the Holocaust, we failed to let refugees like Anne Frank into our country. We can't let history repeat itself," she said.
Malala Yousafzai, the teenage Nobel Peace Laureate who was shot by the Taliban following her advocacy for women's education in Pakistan, wrote that she was "heartbroken".
"America is turning its back on a proud history of welcoming refugees and immigrants - the people who helped build your country, ready to work hard in exchange for a fair chance at a new life," she added.
The head of American Civil Liberties Union (ACLU) condemned the use of the words "extreme vetting", saying it was a "euphemism for discriminating against Muslims".
"Identifying specific countries with Muslim majorities and carving out exceptions for minority religions flies in the face of the constitutional principle that bans the government from either favouring or discriminating against particular religions," Anthony Romero
said in a statement.
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